List questions from divisibility

Published on 14 Apr 2014 - 0:43

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Coprimality of $2^n + 3^n$ and $5^n + 7^n$

Published on 14 Apr 2014 - 4:24

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Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$

Published on 27 Mar 2026 - 21:19

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GCD of $a^n + b^n$ and $c^n + d^n$

Published on 14 Apr 2014 - 11:27

131

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For any integer $a$, $\gcd(11a+5,2a+1)=1$.

Published on 15 Apr 2014 - 0:29

227

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Greatest common divisor and exponent relationship

Published on 15 Apr 2014 - 0:30

259

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Prove that $a^7-a$ is divisible by 168 when a is odd

Published on 15 Apr 2014 - 4:36

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Optimal strategy in Euclid's game

Published on 15 Apr 2014 - 7:04

50

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Is my proof correct? Let $a, b, c\in\mathbb Z$. Prove that if $a\mid b$ and $b\mid c$, then $a\mid(b + c)$.

Published on 15 Apr 2014 - 8:25

209

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Proof on Divisibility of Binomial Coefficients

Published on 15 Apr 2014 - 15:20

48

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Find all positive integers n such that $n\mid\lfloor(n-1)!/(n+1)\rfloor$

Published on 16 Apr 2014 - 19:15

9.7k

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The product of three consecutive natural numbers is divisible by $6$

Published on 17 Apr 2014 - 5:47

62

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An exercise regarding polynomials

Published on 17 Apr 2014 - 10:32

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Show that $(x + 1)^{(2n + 1)} + x^{(n + 2)}$ can be divided by $x^2 + x + 1$ without remainder

Published on 17 Apr 2014 - 12:22

286

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Curious number theory problem

Published on 17 Apr 2014 - 13:13

List Question

Let $n\ge 2$ be an integer. If $\gcd(a,b^n)=1$, then $\gcd(a,b)=1$

Coprimality of $2^n + 3^n$ and $5^n + 7^n$

Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$

GCD of $a^n + b^n$ and $c^n + d^n$

For any integer $a$, $\gcd(11a+5,2a+1)=1$.

Greatest common divisor and exponent relationship

Prove that $a^7-a$ is divisible by 168 when a is odd

Optimal strategy in Euclid's game

Is my proof correct? Let $a, b, c\in\mathbb Z$. Prove that if $a\mid b$ and $b\mid c$, then $a\mid(b + c)$.

Proof on Divisibility of Binomial Coefficients

Find all positive integers n such that $n\mid\lfloor(n-1)!/(n+1)\rfloor$

The product of three consecutive natural numbers is divisible by $6$

An exercise regarding polynomials

Show that $(x + 1)^{(2n + 1)} + x^{(n + 2)}$ can be divided by $x^2 + x + 1$ without remainder

Curious number theory problem

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