List questions from divisibility

Published on 28 Sep 2015 - 15:35

71

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How to prove: if $a$ is an even integer, $\gcd(a^3 - 1, a + 1) = 1$

Published on 12 Apr 2026 - 5:10

125

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Looking applications for these statements involving multiplicative functions and Euler-Fermat theorem

Published on 25 Mar 2026 - 21:22

193

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Is 7^2015 + 4^2015 divisible by 17? Explain your reasoning and show your work.

Published on 13 Apr 2026 - 2:24

348

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Proof that $3^c + 7^c - 2$ by induction

Published on 30 Sep 2015 - 3:44

285

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How to prove that $7^{15} + 7^{16} + 7^{17} - 1$ is divisible by $10$?

Published on 01 Oct 2015 - 7:47

210

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How to prove if $m,n\in \mathbb{Z}$,then $30\mid mn(m^4 -n^4)$

Published on 30 Mar 2026 - 5:30

263

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If $3|(a^2 + b^2)$, show that $3|a$ and $3|b$.

Published on 28 Mar 2026 - 12:48

1.3k

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Prove $\gcd\left(\frac{a^m - 1}{a -1},a -1\right) = \gcd(m,a-1)$

Published on 03 Apr 2026 - 9:28

206

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Palindromes and LCM

Published on 13 Apr 2026 - 7:51

43

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Is my limited understanding of division and gcd on track?

Published on 11 Apr 2026 - 13:25

429

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If $n \mid a^2 $, what is the largest $m$ for which $m \mid a$?

Published on 13 Apr 2026 - 7:58

398

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Prove that $GCD(a,b)=1$ if for all natural numbers $c, a|bc $ then $a|c$.

Published on 03 Apr 2026 - 9:38

1.3k

Views

LCM of $n$ consecutive natural numbers

Published on 11 Apr 2026 - 19:57

353

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Proof that $n+k+3$ divides $n(n+1)(n+2)(n+3) - k(k+1)(k+2)(k+3)$.

Published on 07 Oct 2015 - 18:35

List Question

Prove that $5\mid 8^n - 3^n$ for $n \ge 1$

How to prove: if $a$ is an even integer, $\gcd(a^3 - 1, a + 1) = 1$

Looking applications for these statements involving multiplicative functions and Euler-Fermat theorem

Is 7^2015 + 4^2015 divisible by 17? Explain your reasoning and show your work.

Proof that $3^c + 7^c - 2$ by induction

How to prove that $7^{15} + 7^{16} + 7^{17} - 1$ is divisible by $10$?

How to prove if $m,n\in \mathbb{Z}$,then $30\mid mn(m^4 -n^4)$

If $3|(a^2 + b^2)$, show that $3|a$ and $3|b$.

Prove $\gcd\left(\frac{a^m - 1}{a -1},a -1\right) = \gcd(m,a-1)$

Palindromes and LCM

Is my limited understanding of division and gcd on track?

If $n \mid a^2 $, what is the largest $m$ for which $m \mid a$?

Prove that $GCD(a,b)=1$ if for all natural numbers $c, a|bc $ then $a|c$.

LCM of $n$ consecutive natural numbers

Proof that $n+k+3$ divides $n(n+1)(n+2)(n+3) - k(k+1)(k+2)(k+3)$.

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