List questions from divisibility

Published on 20 Sep 2014 - 18:40

299

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The only positive divisor of both $a$ and $a + 1 $ is $1$

Published on 22 Sep 2014 - 0:16

1.2k

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Proof that the greatest common divisor of $(a, a+2)$ is $2$ if $a$ is even and $1$ if $a$ is odd

Published on 22 Sep 2014 - 3:56

62

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The divisibility of the values of quadratic polynomials in $x$, for integer $x$

Published on 22 Sep 2014 - 10:57

154

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Prove or disprove $ p^{r+s}\mid q^{ke} - 1 \iff p^s \mid k$.

Published on 23 Sep 2014 - 5:51

57

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How to prove $\gcd(a+m,b)=d$ when given $\gcd(a,b)=d$ and $b|m$?

Published on 23 Sep 2014 - 11:28

96

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General Rule for calculating solutions to $ax+by=1$ where $(a,b)=1$

Published on 28 Mar 2026 - 0:48

2.6k

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Find a 4-digit number which, divided by a 3-digit number (all unique digits) equals 9

Published on 24 Sep 2014 - 4:10

3.7k

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Number of divisors of huge numbers

Published on 24 Sep 2014 - 16:58

187

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Modular arithmetic

Published on 24 Sep 2014 - 17:01

210

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Does there always exist an even $m$ that is a multiple of exactly $n$ of the numbers $1$, $2$, ..., $2n$?

Published on 24 Sep 2014 - 19:30

150

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Solve using Linear Congruences and Divisibility.

Published on 26 Mar 2026 - 6:18

69

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Question about $\gcd$

Published on 25 Sep 2014 - 22:32

298

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a proof of contradiction

Published on 27 Sep 2014 - 4:33

4.6k

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Proving $\phi(m)|\phi(n)$ whenever $m|n$

Published on 25 Mar 2026 - 19:01

List Question

Part of a proof that the product of an odd and even integers is even

The only positive divisor of both $a$ and $a + 1 $ is $1$

Proof that the greatest common divisor of $(a, a+2)$ is $2$ if $a$ is even and $1$ if $a$ is odd

The divisibility of the values of quadratic polynomials in $x$, for integer $x$

Prove or disprove $ p^{r+s}\mid q^{ke} - 1 \iff p^s \mid k$.

How to prove $\gcd(a+m,b)=d$ when given $\gcd(a,b)=d$ and $b|m$?

General Rule for calculating solutions to $ax+by=1$ where $(a,b)=1$

Find a 4-digit number which, divided by a 3-digit number (all unique digits) equals 9

Number of divisors of huge numbers

Modular arithmetic

Does there always exist an even $m$ that is a multiple of exactly $n$ of the numbers $1$, $2$, ..., $2n$?

Solve using Linear Congruences and Divisibility.

Question about $\gcd$

a proof of contradiction

Proving $\phi(m)|\phi(n)$ whenever $m|n$

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