List questions from divisibility

Published on 21 Mar 2026 - 23:06

138

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Divisibility transitive proof

Published on 22 Mar 2026 - 12:50

830

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Proof involving linear combinations and gcd of two numbers

Published on 22 Mar 2026 - 14:26

828

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If c = gcd(a, b), prove that gcd( a/c , b/c ) = 1

Published on 17 Mar 2026 - 16:35

832

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Positive Integer Divison Proof

Published on 17 Mar 2026 - 9:15

73

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How show that $40 \mid n.$

Published on 16 Mar 2026 - 21:37

41

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Proof of inequality involving positive number

Published on 17 Mar 2026 - 14:06

131

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Proving $(n!)^n | (n^2)!$

Published on 20 Mar 2026 - 2:12

73

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What are the most used divisibility theorems?

Published on 20 Mar 2026 - 12:07

3.6k

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Prove that $2^{5n + 1} + 5^{n + 2} $ is divisible by 27 for any positive integer

Published on 08 Feb 2018 - 19:51

362

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Let $a, b, c, d$ be positive integers satisfying $ab=cd$. Prove that $a+b+c+d$ ݀ is composite.

Published on 23 Mar 2026 - 12:38

46

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Theorem on greatest common divisor

Published on 17 Mar 2026 - 2:49

30

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Prove that $kn+r$ isn't divisible by $k$ if $r$ isn't divisible by $k$ and $k$,$n$ and $r$ are integers.

Published on 11 Feb 2018 - 18:18

89

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If $a\mid b$ and $a\mid c$ prove $a\mid a^2 + 3b - 2^{b} c$

Published on 11 Feb 2018 - 20:37

62

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Prove that $a_1a_2 ≡ b_1b_2 \mod n$

Published on 13 Feb 2018 - 3:20

List Question

If $(a,b)=1$, then $ \gcd(a^2+b^2,a^3+b^3)\mid (a-b)$

Divisibility transitive proof

Proof involving linear combinations and gcd of two numbers

If c = gcd(a, b), prove that gcd( a/c , b/c ) = 1

Positive Integer Divison Proof

How show that $40 \mid n.$

Proof of inequality involving positive number

Proving $(n!)^n | (n^2)!$

What are the most used divisibility theorems?

Prove that $2^{5n + 1} + 5^{n + 2} $ is divisible by 27 for any positive integer

Let $a, b, c, d$ be positive integers satisfying $ab=cd$. Prove that $a+b+c+d$ ݀ is composite.

Theorem on greatest common divisor

Prove that $kn+r$ isn't divisible by $k$ if $r$ isn't divisible by $k$ and $k$,$n$ and $r$ are integers.

If $a\mid b$ and $a\mid c$ prove $a\mid a^2 + 3b - 2^{b} c$

Prove that $a_1a_2 ≡ b_1b_2 \mod n$

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