List questions from divisibility

Published on 08 Mar 2015 - 3:02

33

Views

Prove the following conditional divisibility

Published on 09 Apr 2026 - 5:32

424

Views

Proof involving gcd and congruence.

Published on 29 Mar 2026 - 6:02

114

Views

Proof with congruence and primes. $(p\mid a^2+b^2)(p\not\mid a,p\not\mid b)\implies \exists c\in\mathbb Z( c^2=-1\pmod {p})$.

Published on 29 Mar 2026 - 5:58

133

Views

Under what conditions is a tower of quadratic extensions a UFD, GCD domain, or just an Integral Domain?

Published on 29 Mar 2026 - 21:02

6.6k

Views

Prove $7$ divides $13^n- 6^n$ for any positive integer

Published on 08 Mar 2015 - 20:29

49

Views

if $p \mid (a^2 + b^2 )$, $p \nmid a$ and $p \nmid b$. Prove that there exists an integer $c$ such that $c^2 \equiv −1 \mod p$.

Published on 29 Mar 2026 - 5:58

188

Views

$ 0 < a < b\,\Rightarrow\, b\bmod p\, <\, a\bmod p\ $ for some prime $p$

Published on 11 Mar 2015 - 18:10

93

Views

Proving if it is prime

Published on 12 Mar 2015 - 0:40

142

Views

What is the point of the common divisibility trick for $7$?

Published on 12 Mar 2015 - 6:00

1.4k

Views

Proof that $2^{222}-1$ is divisible by 3

Published on 12 Mar 2015 - 13:34

221

Views

Common divisor of $a+b$ and $ab$.

Published on 12 Mar 2015 - 17:38

51

Views

Testing the divisibility of $\sum_{k=0}^{m-1} (n+k) $ by $m$ when $m$ is odd

Published on 12 Mar 2015 - 22:20

724

Views

If $\gcd(a,b)=1$ then $\gcd(a^2+b^2,a+2ab)=1$ or $5$

Published on 13 Mar 2015 - 10:16

2.3k

Views

Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.

Published on 28 Mar 2026 - 2:23

List Question

$2n\choose n$ is divisible by all the primes between $10$ and $30$.

Prove the following conditional divisibility

Proof involving gcd and congruence.

Proof with congruence and primes. $(p\mid a^2+b^2)(p\not\mid a,p\not\mid b)\implies \exists c\in\mathbb Z( c^2=-1\pmod {p})$.

Under what conditions is a tower of quadratic extensions a UFD, GCD domain, or just an Integral Domain?

Prove $7$ divides $13^n- 6^n$ for any positive integer

if $p \mid (a^2 + b^2 )$, $p \nmid a$ and $p \nmid b$. Prove that there exists an integer $c$ such that $c^2 \equiv −1 \mod p$.

$ 0 < a < b\,\Rightarrow\, b\bmod p\, <\, a\bmod p\ $ for some prime $p$

Proving if it is prime

What is the point of the common divisibility trick for $7$?

Proof that $2^{222}-1$ is divisible by 3

Common divisor of $a+b$ and $ab$.

Testing the divisibility of $\sum_{k=0}^{m-1} (n+k) $ by $m$ when $m$ is odd

If $\gcd(a,b)=1$ then $\gcd(a^2+b^2,a+2ab)=1$ or $5$

Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.

Trending Questions

Popular # Hahtags

Popular Questions