# Recent questions tagged integers

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$\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}$ are positive integers
$\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}$ are positive integers$\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}$ are positive integers abcde $=a+b+c+d+e$ $\max (\max (a, b, c, d, e))=?$ ...
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Does MathsGee have a Number Line: Integers simulation?
Does MathsGee have a Number Line: Integers simulation?Does MathsGee have a Number Line: Integers simulation? ...
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Write down the number of integers that satisfy the inequality $-11\leq 3m-8\leq 4$
Write down the number of integers that satisfy the inequality $-11\leq 3m-8\leq 4$Write down the number of integers that satisfy the inequality $-11\leq 3m-8\leq 4$ ...
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What are all sets of three positive consecutive even integers such that twice the sum of the two is less than three several times the third?
What are all sets of three positive consecutive even integers such that twice the sum of the two is less than three several times the third?What are all sets of three positive consecutive even integers such that twice the sum of the two is less than three several times the third? ...
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Prove the following theorem:
Prove the following theorem:Prove the following theorem: Let $n$ and $m$ be integers. Then i. if $n$ and $m$ are both even, then $n+m$ is even, ii. if $n$ and $m$ ...
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Simplify $\frac{1}{7} \times \frac{9}{16} \times \frac{16}{9} \times \frac{16}{9} \times \frac{9}{16}=$
Simplify $\frac{1}{7} \times \frac{9}{16} \times \frac{16}{9} \times \frac{16}{9} \times \frac{9}{16}=$Simplify $\frac{1}{7} \times \frac{9}{16} \times \frac{16}{9} \times \frac{16}{9} \times \frac{9}{16}=$ ...
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Are there lots of integer solutions for the mysterious equation, or just a few? $n! + n = n^n$
Are there lots of integer solutions for the mysterious equation, or just a few? $n! + n = n^n$Are there lots of integer solutions for the mysterious equation below, or just a few? \ n! + n = n^n\ ...
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Show that $x^{2}-6 x+11>0$ for all real values of $x$.
Show that $x^{2}-6 x+11>0$ for all real values of $x$.Show that $x^{2}-6 x+11&gt;0$ for all real values of $x$. ...
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Find the value of $x$ such that $\frac{1+x}{x}=\sqrt{5}$ Giving your answer in the form $a+b \sqrt{5}$ where $a$ and $b$ are rational numbers.
Find the value of $x$ such that $\frac{1+x}{x}=\sqrt{5}$ Giving your answer in the form $a+b \sqrt{5}$ where $a$ and $b$ are rational numbers.Find the value of $x$ such that \ \frac{1+x}{x}=\sqrt{5} \ Giving your answer in the form $a+b \sqrt{5}$ where $a$ and $b$ are rational numb ...
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Factorise completely: $75 x-12 x^{3}$
Factorise completely: $75 x-12 x^{3}$Factorise completely: $75 x-12 x^{3}$ ...
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Factorise completely: $x-16 x^{3}$
Factorise completely: $x-16 x^{3}$Factorise completely: $x-16 x^{3}$ ...
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Given $y=2^{x}$ - Express $4^{x}$ in terms of $y$.
Given $y=2^{x}$ - Express $4^{x}$ in terms of $y$.Given $y=2^{x}$ (a) Express $4^{x}$ in terms of $y$. (b) Hence, or otherwise, solve $4^{x}-6\left(2^{x}\right)-16=0$ ...
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Express $8^{2 x-5}$ in the form $2^{y}$, giving $y$ in the form $a x+b$, where $a$ and $b$ are constants.
Express $8^{2 x-5}$ in the form $2^{y}$, giving $y$ in the form $a x+b$, where $a$ and $b$ are constants.Express $8^{2 x-5}$ in the form $2^{y}$, giving $y$ in the form $a x+b$, where $a$ and $b$ are constants. ...
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Express $9^{3 x+2}$ in the form $3^{y}$, giving $y$ in the form $a x+b$, where $a$ and $b$ are constants.
Express $9^{3 x+2}$ in the form $3^{y}$, giving $y$ in the form $a x+b$, where $a$ and $b$ are constants.Express $9^{3 x+2}$ in the form $3^{y}$, giving $y$ in the form $a x+b$, where $a$ and $b$ are constants. ...
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Determine the value of m
Determine the value of mIf $m$ is the largest integer for which $m^{200} &lt; 5^{300}$, determine the value of $m$ ...
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$\alpha$ and $\beta$ are the roots of the equation $2 x^{2}-3 x+4=0$. Find $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$
$\alpha$ and $\beta$ are the roots of the equation $2 x^{2}-3 x+4=0$. Find $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$$\alpha$ and $\beta$ are the roots of the equation $2 x^{2}-3 x+4=0$. Find $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$ A. $\frac{-9}{8}$ B. ...
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$\alpha$ and $\beta$ are the roots of the equation $2 x^{2}-3 x+4=0$. Find $\alpha+\beta$
$\alpha$ and $\beta$ are the roots of the equation $2 x^{2}-3 x+4=0$. Find $\alpha+\beta$$\alpha$ and $\beta$ are the roots of the equation $2 x^{2}-3 x+4=0$. Find $\alpha+\beta$ A. $-2$ B. $-\frac{3}{2}$ C. $\frac{3}{2}$ D. ...
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What is the prime factorization of 136?
Prove that there exist 3 indices $p, q$ and $r$ such that $p<q<r$ and
Prove that there exist 3 indices $p, q$ and $r$ such that $p<q<r$ andProve that there exist 3 indices $p, q$ and $r$ such that $p&lt;q&lt;r$ and \begin{gathered} a_{p} \leq a_{q} \leq a_{r} \\ b_{p} \leq b_{q} \leq ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 When are two complex numbers equal? 1 answer 270 views When are two complex numbers equal?When are two complex numbers equal? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Can integers be written as rational numbers? 1 answer 90 views Can integers be written as rational numbers? Write each of the following as a rational number. 7 0 -8 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 A(n) __________________ is an arrangement of numbers in rows and columns. 0 answers 86 views A(n) __________________ is an arrangement of numbers in rows and columns.A(n) __________________ &nbsp;is an arrangement of numbers in rows and columns. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. 1 answer 186 views Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n.Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23)=6 and S(23)=5. Suppose N ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Express b \times b \times b \times b \times b in exponential form: 1 answer 171 views Express b \times b \times b \times b \times b in exponential form:Express b \times b \times b \times b \times b in exponential form: ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 How many positive integers n satisfy the inequality 2000<\sqrt{n(n+1)}<2016 ? 0 answers 181 views How many positive integers n satisfy the inequality 2000<\sqrt{n(n+1)}<2016 ?How many positive integers n satisfy the inequality 2000&lt;\sqrt{n(n+1)}&lt;2016 ? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 For how many integers n is 72\left(\frac{3}{2}\right)^{n} equal to an integer? 0 answers 133 views For how many integers n is 72\left(\frac{3}{2}\right)^{n} equal to an integer?For how many integers n is 72\left(\frac{3}{2}\right)^{n} equal to an integer? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Two positive integers m and n satisfy the equation m^{2} n=2016. How many different values of m are possible? 0 answers 157 views Two positive integers m and n satisfy the equation m^{2} n=2016. How many different values of m are possible?Two positive integers m and n satisfy the equation m^{2} n=2016. How many different values of m are possible? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 How many integers satisfy the equation 2^{x}(6-x)=8 x ? 0 answers 93 views How many integers satisfy the equation 2^{x}(6-x)=8 x ?How many integers satisfy the equation 2^{x}(6-x)=8 x ? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 How many odd integers are there between \frac{17}{4} and \frac{47}{2} ? 0 answers 112 views How many odd integers are there between \frac{17}{4} and \frac{47}{2} ?How many odd integers are there between \frac{17}{4} and \frac{47}{2} ? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 How are complex numbers related to real numbers? 1 answer 176 views How are complex numbers related to real numbers?How are complex numbers related to real numbers? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 For how many integers x is the fraction \frac{4 x-17}{5 x+9} also an integer? 0 answers 245 views For how many integers x is the fraction \frac{4 x-17}{5 x+9} also an integer?For how many integers x is the fraction \frac{4 x-17}{5 x+9} also an integer? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If { }^{n} P_{r}:{ }^{n} C_{r}=126 then find n and r. 0 answers 108 views If { }^{n} P_{r}:{ }^{n} C_{r}=126 then find n and r.If { }^{n} P_{r}:{ }^{n} C_{r}=126 then find n and r. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the number of rectangles and squares in an 8 by 8 chess board respectively. 0 answers 418 views Find the number of rectangles and squares in an 8 by 8 chess board respectively.Find the number of rectangles and squares in an 8 by 8 chess board respectively. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 For how many integers n is the fraction \frac{2 n^{2}+1}{n^{2}-1} also an integer? 0 answers 2K views For how many integers n is the fraction \frac{2 n^{2}+1}{n^{2}-1} also an integer?For how many integers n is the fraction \frac{2 n^{2}+1}{n^{2}-1} also an integer? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 When is the expression \sqrt{a} real? 1 answer 77 views When is the expression \sqrt{a} real?When is the expression \sqrt{a} real? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve for x: 9^{x+1}=27^{x} 1 answer 112 views Solve for x: 9^{x+1}=27^{x}Solve for x: 9^{x+1}=27^{x} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Express 9^{x-1}+3^{2 x} as a single power expression. 1 answer 116 views Express 9^{x-1}+3^{2 x} as a single power expression.Express 9^{x-1}+3^{2 x} as a single power expression. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If \alpha and \beta are the roots of the equation x^{2}-x+1=0, then \alpha^{2009}+\beta^{2009}= 1 answer 240 views If \alpha and \beta are the roots of the equation x^{2}-x+1=0, then \alpha^{2009}+\beta^{2009}=If \alpha and \beta are the roots of the equation x^{2}-x+1=0, then \alpha^{2009}+\beta^{2009}= 1) -1 2) 1 3) 2 4) -2 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Difference between the corresponding roots of x^{2}+a x+b=0 and x^{2}+b x+a=0 is same and a \neq b, then 1 answer 117 views Difference between the corresponding roots of x^{2}+a x+b=0 and x^{2}+b x+a=0 is same and a \neq b, thenDifference between the corresponding roots of x^{2}+a x+b=0 and x^{2}+b x+a=0 is same and a \neq b, then 1) a+b+4=0 2) a+b-4=0 3) a-b-4=0 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If \alpha \neq \beta but \alpha^{2}=5 \alpha-3 and \beta^{2}=5 \beta-3 then the equation having \frac{\alpha}{\beta} and \frac{\beta}{\alpha} as its roots is 1 answer 236 views If \alpha \neq \beta but \alpha^{2}=5 \alpha-3 and \beta^{2}=5 \beta-3 then the equation having \frac{\alpha}{\beta} and \frac{\beta}{\alpha} as its roots isIf \alpha \neq \beta but \alpha^{2}=5 \alpha-3 and \beta^{2}=5 \beta-3 then the equation having \dfrac{\alpha}{\beta} and \dfrac{\beta}{\alph ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If z \neq 1 and \frac{z^{2}}{z-1} is real, then the point represented by the complex number \mathrm{z} lies 1 answer 110 views If z \neq 1 and \frac{z^{2}}{z-1} is real, then the point represented by the complex number \mathrm{z} liesIf z \neq 1 and \frac{z^{2}}{z-1} is real, then the point represented by the complex number \mathrm{z} lies 1) either on the real axis or on a ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let \alpha, \beta be real and z be a complex number. If z^{2}+\alpha z+\beta=0 has two distinct roots on the line \operatorname{Re} z=1, then it is necessary that 1 answer 136 views Let \alpha, \beta be real and z be a complex number. If z^{2}+\alpha z+\beta=0 has two distinct roots on the line \operatorname{Re} z=1, then it is necessary thatLet \alpha, \beta be real and z be a complex number. If z^{2}+\alpha z+\beta=0 has two distinct roots on the line \operatorname{Re} z=1, then ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The number of complex number z such that |z-1|=|z+1|=|z-i| equals 1 answer 238 views The number of complex number z such that |z-1|=|z+1|=|z-i| equalsThe number of complex number z such that |z-1|=|z+1|=|z-i| equals 1) 1 2) 2 3) \infty 4) 0 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If z^{2}+z+1=0, where z is a complex number, then the value of 1 answer 182 views If z^{2}+z+1=0, where z is a complex number, then the value ofIf z^{2}+z+1=0, where z is a complex number, then the value of \begin{aligned}\left(z+\frac{1}{z}\right)^{2}+\left(z^{2}+\frac{1}{z^{2}}\right)^ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If z_{1} and z_{2} are two non-zero complex numbers such that \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right| then \arg z_{1}-\arg z_{2} is equal to 1 answer 379 views If z_{1} and z_{2} are two non-zero complex numbers such that \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right| then \arg z_{1}-\arg z_{2} is equal to If z_{1} and z_{2} are two non-zero complex numbers such that \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right| then \arg z_{1}-\a ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let z, w be complex numbers such that \bar{z}+i \bar{w}=0 and \arg z w=\pi . Then arg z equals 1 answer 128 views Let z, w be complex numbers such that \bar{z}+i \bar{w}=0 and \arg z w=\pi . Then arg z equalsLet z, w be complex numbers such that \bar{z}+i \bar{w}=0 and \arg z w=\pi . Then arg z equals 1) \frac{\pi}{4} 2) \frac{5 \pi}{4} 3) \f ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If z and w are two non-zero complex numbers such that |z w|=1, and \operatorname{Arg}(z)-\operatorname{Arg}(w)=\frac{\pi}{2}, then \bar{z} \omega is equal to 1 answer 171 views If z and w are two non-zero complex numbers such that |z w|=1, and \operatorname{Arg}(z)-\operatorname{Arg}(w)=\frac{\pi}{2}, then \bar{z} \omega is equal toIf z and w are two non-zero complex numbers such that |z w|=1, and \operatorname{Arg}(z)-\operatorname{Arg}(w)=\dfrac{\pi}{2}, then \bar{z} \ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 z and w are two non zero complex no.s such that |z|=|w| and \operatorname{Arg} z+A r g w=\pi then z equals 1 answer 104 views z and w are two non zero complex no.s such that |z|=|w| and \operatorname{Arg} z+A r g w=\pi then z equalsz and w are two non zero complex no.s such that |z|=|w| and \operatorname{Arg} z+A r g w=\pi then z equals 1) \bar{w} 2) -\bar{w} 3) w ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let n be a positive integer. Show that \left(1+\frac{1}{n+1}\right)^{n+1}>\left(1+\frac{1}{n}\right)^{n}. 0 answers 179 views Let n be a positive integer. Show that \left(1+\frac{1}{n+1}\right)^{n+1}>\left(1+\frac{1}{n}\right)^{n}.Let n be a positive integer. Show that \left(1+\frac{1}{n+1}\right)^{n+1}&gt;\left(1+\frac{1}{n}\right)^{n}. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let n>1 be an integer. Show that n !<\left(\frac{n+1}{2}\right)^{n} $$1 answer 152 views Let n>1 be an integer. Show that$$ n !<\left(\frac{n+1}{2}\right)^{n} $$Let n&gt;1 be an integer. Show that$$ n !&lt;\left(\frac{n+1}{2}\right)^{n}  ...