List questions from divisibility

Published on 07 Oct 2015 - 21:06

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If a divisor of $pq-1$ divides the LCM of $p-1$ and $q-1$, then it also divides the GCD of these two numbers

Published on 11 Apr 2026 - 19:57

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Prove divisibility with gcd: If $ar+bs=d=\gcd(a,b)$, then $r$ and $s$ are relatively prime

Published on 03 Apr 2026 - 9:38

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Simple question about dividing by zero, $y=\frac{x}{x}$ when $x=0$

Published on 13 Apr 2026 - 9:14

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if $5\nmid a$ or $5\nmid b$, then $5\nmid a^2-2b^2$.

Published on 28 Mar 2026 - 12:48

208

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Divisibility of subsets of the set $1, 2, 3, ..., n$

Published on 03 Apr 2026 - 11:06

163

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Unwind quaternion multiplication

Published on 25 Mar 2026 - 23:35

68

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Prove $3 \mid x-2 \implies 3 \mid (x^2 - x+1)$ using division algorithm

Published on 09 Oct 2015 - 20:14

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Showing that if $(a,b)=1$ and if $a\mid c$ and $b\mid c$ then $ab \mid c$, in GCD domains

Published on 13 Apr 2026 - 1:00

194

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subtract two 4-digit numbers and obtain the sum of the digits always 18

Published on 12 Apr 2026 - 20:04

206

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Efficient way to check if large number is divisible by 3

Published on 18 Mar 2026 - 23:48

90

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Only prime numbers $a$ (and $1$) have the property that $a\mid bc$ implies $a\mid b$ or $a\mid c$

Published on 01 Apr 2026 - 0:52

651

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Divisibility proof with co-prime numbers

Published on 26 Feb 2026 - 12:36

2.9k

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Prove that if 2 divides $x^2-5$ then 4 divides $x^2-5$

Published on 28 Mar 2026 - 23:21

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Number Theory Homework: Find 3 consecutive integers...

Published on 30 Mar 2026 - 7:10

List Question

Prove that $AB\mid CD$

If a divisor of $pq-1$ divides the LCM of $p-1$ and $q-1$, then it also divides the GCD of these two numbers

Prove divisibility with gcd: If $ar+bs=d=\gcd(a,b)$, then $r$ and $s$ are relatively prime

Simple question about dividing by zero, $y=\frac{x}{x}$ when $x=0$

if $5\nmid a$ or $5\nmid b$, then $5\nmid a^2-2b^2$.

Divisibility of subsets of the set $1, 2, 3, ..., n$

Unwind quaternion multiplication

Prove $3 \mid x-2 \implies 3 \mid (x^2 - x+1)$ using division algorithm

Showing that if $(a,b)=1$ and if $a\mid c$ and $b\mid c$ then $ab \mid c$, in GCD domains

subtract two 4-digit numbers and obtain the sum of the digits always 18

Efficient way to check if large number is divisible by 3

Only prime numbers $a$ (and $1$) have the property that $a\mid bc$ implies $a\mid b$ or $a\mid c$

Divisibility proof with co-prime numbers

Prove that if 2 divides $x^2-5$ then 4 divides $x^2-5$

Number Theory Homework: Find 3 consecutive integers...

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