List questions from divisibility

Published on 12 Nov 2014 - 20:23

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Prove that $\big( n^2 - 1 \big) \mid \big( 2^{n!} - 1 \big) $

Published on 12 Nov 2014 - 21:03

717

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Proving a polynomial is not divisible

Published on 13 Nov 2014 - 18:47

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Divisibility problem using DFA

Published on 26 Mar 2026 - 23:57

82

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Prove divisibility: $6\mid 13^n+7^n-2$

Published on 14 Nov 2014 - 19:37

72

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Is there an $n$ such that $p|n^2+1$ with $2n<p<2n+\sqrt n$?

Published on 31 Mar 2026 - 8:12

434

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Proof by Induction: for all integers n $\ge$ 0, $12\mid8^{2n+1}+2^{4n+2}$

Published on 15 Nov 2014 - 5:21

70

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Strategy for solving $7\vert2^{n+2}+3^{2n+1}$ by induction.

Published on 15 Nov 2014 - 14:59

246

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Prove $\operatorname{lcm}(a, b) = ab / \gcd(a,b);\ $ $\gcd(a,b) \le |a - b|$ for $a \ne b$

Published on 15 Nov 2014 - 17:03

47

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If p is a prime what values of $ a\leq p^{n}$ have $\text{gcd}(a, p^{n}) >1$?

Published on 15 Nov 2014 - 21:03

791

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Consider the relation R given by divisibility on positive integers that is xRy <-> x|y

Published on 29 Mar 2026 - 18:53

8.2k

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How to find the number of divisors that are perfect squares and divisible by a number

Published on 16 Nov 2014 - 10:25

192

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Number theory,GCD, coprime integers

Published on 16 Nov 2014 - 13:11

9.3k

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Prove that $\gcd(2^a - 1, 2^b - 1) = 2^{\gcd(a,b)} - 1$

Published on 16 Nov 2014 - 16:43

1.5k

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Prove that if $a$ divides $ b$ , and $a$ divides $b + 2$ then $a = 1$ or $ a = 2$.

Published on 16 Nov 2014 - 20:59

List Question

Divisors $1\bmod 4$ more than $3\bmod 4$

Prove that $\big( n^2 - 1 \big) \mid \big( 2^{n!} - 1 \big) $

Proving a polynomial is not divisible

Divisibility problem using DFA

Prove divisibility: $6\mid 13^n+7^n-2$

Is there an $n$ such that $p|n^2+1$ with $2n<p<2n+\sqrt n$?

Proof by Induction: for all integers n $\ge$ 0, $12\mid8^{2n+1}+2^{4n+2}$

Strategy for solving $7\vert2^{n+2}+3^{2n+1}$ by induction.

Prove $\operatorname{lcm}(a, b) = ab / \gcd(a,b);\ $ $\gcd(a,b) \le |a - b|$ for $a \ne b$

If p is a prime what values of $ a\leq p^{n}$ have $\text{gcd}(a, p^{n}) >1$?

Consider the relation R given by divisibility on positive integers that is xRy <-> x|y

How to find the number of divisors that are perfect squares and divisible by a number

Number theory,GCD, coprime integers

Prove that $\gcd(2^a - 1, 2^b - 1) = 2^{\gcd(a,b)} - 1$

Prove that if $a$ divides $ b$ , and $a$ divides $b + 2$ then $a = 1$ or $ a = 2$.

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