Question

Proof that $a|b \iff ac|bc$

score 3.1k · Answer 1 · 2018-06-23 22:23:07

3.1k

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Proof that $a|b \iff ac|bc$

Published on 23 Jun 2018 - 22:23

score 97 · Answer 2 · 2018-06-26 00:56:44

97

Views

Prove by contraditcion that $a\mid b$ then $ac\mid bc$

Published on 26 Jun 2018 - 0:56

score 58 · Answer 3 · 2026-03-25 12:54:29

58

Views

Fast way to count how many numbers less than a given one are not divisible by any prime from a given set

Published on 25 Mar 2026 - 12:54

score 60 · Answer 4 · 2026-03-25 06:05:14

60

Views

Around the equation $4\,\varphi \left(2^{n-1} \sigma(n)\right) ^2=2^{\sigma(n)}\cdot\varphi(n)^2$

Published on 25 Mar 2026 - 6:05

score 117 · Answer 5 · 2018-06-28 11:45:16

117

Views

how to prove that $ax + b$ is not divisible by $cx$

Published on 28 Jun 2018 - 11:45

score 33 · Answer 6 · 2018-06-29 06:43:06

33

Views

Subfields of the finite field: Is divisibility of multiplication groups a sufficient condition?

Published on 29 Jun 2018 - 6:43

score 148 · Answer 7 · 2018-07-02 04:48:23

148

Views

If $a \mid b^2$, $b \mid c^2$, $c \mid a^2$ then prove $abc \mid (a+b+c)^7$

Published on 02 Jul 2018 - 4:48

score 249 · Answer 8 · 2018-07-02 14:58:17

249

Views

Prove that $5^{2^n} - 1$ is divisible by $2^{n+1}$ for all $n ≥ 1$

Published on 02 Jul 2018 - 14:58

score 194 · Answer 9 · 2018-07-02 18:43:40

194

Views

Prove that there are no non-zero integers $m$ and $n$ such that $m^2 = 180 n^4$

Published on 02 Jul 2018 - 18:43

score 929 · Answer 10 · 2018-07-03 10:32:48

929

Views

Remainder on division with $22$

Published on 03 Jul 2018 - 10:32

score 541 · Answer 11 · 2018-07-02 21:26:45

541

Views

Prove that for all integers $a$ and $b$, if $a\mid b$ then $a^2\mid 3b^2$

Published on 02 Jul 2018 - 21:26

score 1.7k · Answer 12 · 2018-07-05 11:11:23

1.7k

Views

Prove by induction: $3^n+1$ is divisible by $2$ for $n\ge 0$

Published on 05 Jul 2018 - 11:11

score 704 · Answer 13 · 2018-07-06 08:53:36

704

Views

When a number is divided by $13$, the remainder is $11$. When the same number is divided by $17$, then remainder is $9$. What is the number?

Published on 06 Jul 2018 - 8:53

score 102 · Answer 14 · 2026-03-25 12:28:17

102

Views

For many integers $n$, the digit sum of $(4n^2+1)^2$ is $19$. Is there something special about $19$?

Published on 25 Mar 2026 - 12:28

score 707 · Answer 15 · 2018-07-12 16:00:53

707

Views

Show that $x^{20}+x^{15}+x^{10}+x^5$ is divisible by $x^2+1$

Published on 12 Jul 2018 - 16:00

List Question

Proof that $a|b \iff ac|bc$

Prove by contraditcion that $a\mid b$ then $ac\mid bc$

Fast way to count how many numbers less than a given one are not divisible by any prime from a given set

Around the equation $4\,\varphi \left(2^{n-1} \sigma(n)\right) ^2=2^{\sigma(n)}\cdot\varphi(n)^2$

how to prove that $ax + b$ is not divisible by $cx$

Subfields of the finite field: Is divisibility of multiplication groups a sufficient condition?

If $a \mid b^2$, $b \mid c^2$, $c \mid a^2$ then prove $abc \mid (a+b+c)^7$

Prove that $5^{2^n} - 1$ is divisible by $2^{n+1}$ for all $n ≥ 1$

Prove that there are no non-zero integers $m$ and $n$ such that $m^2 = 180 n^4$

Remainder on division with $22$

Prove that for all integers $a$ and $b$, if $a\mid b$ then $a^2\mid 3b^2$

Prove by induction: $3^n+1$ is divisible by $2$ for $n\ge 0$

When a number is divided by $13$, the remainder is $11$. When the same number is divided by $17$, then remainder is $9$. What is the number?

For many integers $n$, the digit sum of $(4n^2+1)^2$ is $19$. Is there something special about $19$?

Show that $x^{20}+x^{15}+x^{10}+x^5$ is divisible by $x^2+1$

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