List questions from divisibility

Published on 06 May 2014 - 19:17

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Ramsey Theory: Showing the existence of a special set of natural numbers.

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Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.

Published on 07 May 2014 - 19:40

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Factors of a perfect square plus one

Published on 08 May 2014 - 3:46

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How to solve the equation $n^2 \equiv 0 \pmod{584}$?

Published on 25 Mar 2026 - 20:15

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Divisibility of sum of powers: $\ 323\mid 20^n+16^n-3^n-1\ $ for which $n?$

Published on 08 May 2014 - 21:57

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If a natural number $x$ is divisible by $3$

Published on 08 May 2014 - 22:33

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How to prove that at least one of $a,b,c,d$ is not divisible by $ad-bc$ if $ad-bc>1$?

Published on 09 May 2014 - 6:47

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Prove that $n$ is divisible by $6$

Published on 10 May 2014 - 12:33

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Euler's Refutation of Fermat's Conjecture

Published on 12 May 2014 - 7:09

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Direct proof that the product of odd integers is odd

Published on 14 May 2014 - 0:22

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WordProblem on factors and remainder theorem

Published on 30 Mar 2026 - 10:55

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Given that $a,b,n$ are positive integers. Assume that for any positive integer $k\neq b, (k-b)\mid(k^n-a)$, the which of the following must be true?

Published on 14 May 2014 - 4:23

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What remainder does $34!$ leave when divided by $71$?

Published on 25 Mar 2026 - 23:08

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How to show $(n-1)^3n^3(n+1)^3$ is divisible by 7 and 9?

Published on 25 Mar 2026 - 21:49

List Question

Remainder question with $6!$ and 7

Ramsey Theory: Showing the existence of a special set of natural numbers.

Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.

Factors of a perfect square plus one

How to solve the equation $n^2 \equiv 0 \pmod{584}$?

Divisibility of sum of powers: $\ 323\mid 20^n+16^n-3^n-1\ $ for which $n?$

If a natural number $x$ is divisible by $3$

How to prove that at least one of $a,b,c,d$ is not divisible by $ad-bc$ if $ad-bc>1$?

Prove that $n$ is divisible by $6$

Euler's Refutation of Fermat's Conjecture

Direct proof that the product of odd integers is odd

WordProblem on factors and remainder theorem

Given that $a,b,n$ are positive integers. Assume that for any positive integer $k\neq b, (k-b)\mid(k^n-a)$, the which of the following must be true?

What remainder does $34!$ leave when divided by $71$?

How to show $(n-1)^3n^3(n+1)^3$ is divisible by 7 and 9?

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