List questions from divisibility

Published on 19 Mar 2017 - 2:00

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Prove: If $(a, p) = 1$ , $0 < a < p$ , then $p$ is prime

Published on 01 Apr 2026 - 14:59

31

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Finding the Order of 5 Numbers

Published on 20 Mar 2017 - 0:02

160

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Assume $d\mid n$ and $\gcd(a,d)=1$. Let $t$ be the product of prime numbers that divide $n$, but don’t divide $a$. Show: $\gcd(a+td,n)=1$.

Published on 01 Apr 2026 - 16:30

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proof by induction that $3^{2n-1} + 2^{2n-1}$ is divisible by $5$

Published on 20 Mar 2017 - 18:47

181

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$3\mid a^3+b^3+c^3$ if only if $3\mid a+b+c $

Published on 21 Mar 2017 - 11:36

141

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Divisibility Rule for 11 Using Identity

Published on 21 Mar 2017 - 21:05

625

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Prove each of these statements from each other $\exists x, y: ax +by = 1$ and $\exists u,v: au = bv + 1 $

Published on 01 Apr 2026 - 16:25

546

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If an integer $n$ is coprime to $6$, then prove that $n^2$ leaves remainder 1 on division by 24

Published on 28 Mar 2026 - 10:24

74

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Prove that for all x $\in \mathbb{N}$ it holds that the number a(n) := $x^2$ + 4x + 3 has a non-trivial divisor

Published on 22 Mar 2017 - 20:33

175

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Proof by Induction involving divisibility

Published on 23 Mar 2017 - 0:17

81

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Finding consecutive numbers.

Published on 23 Mar 2017 - 22:20

166

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Divisibility Problem: How many switches remain in their initial position?

Published on 30 Mar 2026 - 13:36

489

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proving the divisibility rule for 11 using induction

Published on 24 Mar 2017 - 17:52

52

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Deduce patterns of divisibility in bit strings

Published on 23 Feb 2026 - 10:43

List Question

Prove $8 \mid n^{n+1} + (n+1)^n - 1$

Prove: If $(a, p) = 1$ , $0 < a < p$ , then $p$ is prime

Finding the Order of 5 Numbers

Assume $d\mid n$ and $\gcd(a,d)=1$. Let $t$ be the product of prime numbers that divide $n$, but don’t divide $a$. Show: $\gcd(a+td,n)=1$.

proof by induction that $3^{2n-1} + 2^{2n-1}$ is divisible by $5$

$3\mid a^3+b^3+c^3$ if only if $3\mid a+b+c $

Divisibility Rule for 11 Using Identity

Prove each of these statements from each other $\exists x, y: ax +by = 1$ and $\exists u,v: au = bv + 1 $

If an integer $n$ is coprime to $6$, then prove that $n^2$ leaves remainder 1 on division by 24

Prove that for all x $\in \mathbb{N}$ it holds that the number a(n) := $x^2$ + 4x + 3 has a non-trivial divisor

Proof by Induction involving divisibility

Finding consecutive numbers.

Divisibility Problem: How many switches remain in their initial position?

proving the divisibility rule for 11 using induction

Deduce patterns of divisibility in bit strings

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