List questions from divisibility

Published on 10 Aug 2016 - 18:21

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Show that $a^j$ has order $(p − 1)/j$ modulo $p$.

Published on 10 Aug 2016 - 21:58

138

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Prove that $112$ divides the integral part of $4^m-(2+\sqrt{2})^m$

Published on 13 Aug 2016 - 15:54

51

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For suitable $a,b$, is it true that $(a+b) \nmid a^{m}$ for all $m \geq 2$?

Published on 04 Apr 2026 - 1:54

147

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Written as sum of positive divisors

Published on 15 Aug 2016 - 7:05

1.1k

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Are half of all numbers even?

Published on 26 Mar 2026 - 1:16

143

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factors of $(x+y)^p-x^p-y^p$

Published on 15 Aug 2016 - 11:30

599

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all poly's such that $P(n)$ divides $2^n-1$

Published on 15 Aug 2016 - 13:04

4.8k

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How to prove if a binary number is divisible by 3?

Published on 31 Mar 2026 - 20:25

363

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Greatest prime divisor of consecutive integers

Published on 17 Aug 2016 - 10:05

191

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Divide line into 3 segments of infinite length

Published on 29 Mar 2026 - 14:57

646

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On divisors of $p^n-1$

Published on 17 Aug 2016 - 20:16

141

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Proof for $\forall n\in \mathbb{N}: 7\mid(1 + 2^{2^n} + 2^{2^{n+1}})$

Published on 18 Aug 2016 - 20:23

47

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Product of divisors plus one

Published on 19 Aug 2016 - 9:05

118

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Find all pairs $(a,b)$ of positive integers, such that $\frac{b^2+ab+a+b-1}{a^2+ab+1}$ is integer.

Published on 20 Aug 2016 - 8:47

List Question

How many positive divisors of 8400 have at least 4 positive divisors?

Show that $a^j$ has order $(p − 1)/j$ modulo $p$.

Prove that $112$ divides the integral part of $4^m-(2+\sqrt{2})^m$

For suitable $a,b$, is it true that $(a+b) \nmid a^{m}$ for all $m \geq 2$?

Written as sum of positive divisors

Are half of all numbers even?

factors of $(x+y)^p-x^p-y^p$

all poly's such that $P(n)$ divides $2^n-1$

How to prove if a binary number is divisible by 3?

Greatest prime divisor of consecutive integers

Divide line into 3 segments of infinite length

On divisors of $p^n-1$

Proof for $\forall n\in \mathbb{N}: 7\mid(1 + 2^{2^n} + 2^{2^{n+1}})$

Product of divisors plus one

Find all pairs $(a,b)$ of positive integers, such that $\frac{b^2+ab+a+b-1}{a^2+ab+1}$ is integer.

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