List questions from divisibility

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A natural number has exactly 10 divisors including 1 and itself.How many distinct prime factors can this natural number have?

Published on 26 Mar 2026 - 2:57

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Why Zero divided by Zero is undefined and not Infinity

Published on 03 Apr 2026 - 12:43

66

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Missing values of the ratio $\frac{(x+y+z)^2}{x^2+y^2+z^2}$

Published on 27 Aug 2015 - 15:22

141

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Difficult sets of Equations, counting

Published on 08 Apr 2026 - 23:04

49

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If $a, b \mid c \text { and } \gcd(a, b) = d, \text { then } ab \mid cd $

Published on 03 Apr 2026 - 4:17

118

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About the least common multiple of numbers and combinatorial

Published on 12 Apr 2026 - 1:45

218

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Divisibility and GCD proof

Published on 31 Aug 2015 - 21:55

146

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Divisibility proof with GCD condition

Published on 11 Apr 2026 - 1:07

58

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Prove $(a, b) \mid ((a + b), (a - b))$

Published on 03 Apr 2026 - 4:16

207

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Lehmer's totient problem generalization (adding a constant )

Published on 11 Apr 2026 - 1:32

80

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Number 9 and age of mother when child is born.

Published on 01 Sep 2015 - 17:11

384

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Number of divisors $d$ of $n^2$ so that $d\nmid n$ and $d>n$

Published on 29 Mar 2026 - 18:15

157

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Proof that expression is integer, $\frac{(2n)!}{n!(n+1)!}$

Published on 03 Apr 2026 - 18:00

21

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If $a, b, c, d \in \mathbb Z$ and $p$ is a prime factor of $a - b$ and $c - d$, then $p$ is a prime factor of $(a + c) - (b + d)$

Published on 03 Sep 2015 - 14:43

126

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$b$ divides $a \Leftrightarrow -b$ divides $a$

Published on 12 Apr 2026 - 8:46

List Question

A natural number has exactly 10 divisors including 1 and itself.How many distinct prime factors can this natural number have?

Why Zero divided by Zero is undefined and not Infinity

Missing values of the ratio $\frac{(x+y+z)^2}{x^2+y^2+z^2}$

Difficult sets of Equations, counting

If $a, b \mid c \text { and } \gcd(a, b) = d, \text { then } ab \mid cd $

About the least common multiple of numbers and combinatorial

Divisibility and GCD proof

Divisibility proof with GCD condition

Prove $(a, b) \mid ((a + b), (a - b))$

Lehmer's totient problem generalization (adding a constant )

Number 9 and age of mother when child is born.

Number of divisors $d$ of $n^2$ so that $d\nmid n$ and $d>n$

Proof that expression is integer, $\frac{(2n)!}{n!(n+1)!}$

If $a, b, c, d \in \mathbb Z$ and $p$ is a prime factor of $a - b$ and $c - d$, then $p$ is a prime factor of $(a + c) - (b + d)$

$b$ divides $a \Leftrightarrow -b$ divides $a$

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