Question

How can I formally prove that $3\mid 2^n+1\iff n=2m+1,m \in \mathbb N$

score 101 · Answer 1 · 2019-06-26 14:59:15

101

Views

How can I formally prove that $3\mid 2^n+1\iff n=2m+1,m \in \mathbb N$

Published on 26 Jun 2019 - 14:59

score 176 · Answer 2 · 2019-06-27 04:40:30

176

Views

Find all natural number $n$ such that $n^2 + 2\mid 2001n + 2$

Published on 27 Jun 2019 - 4:40

score 121 · Answer 3 · 2019-06-27 19:07:29

121

Views

Prime Numbers. Show that if $a \mid 42n + 37$ and $a \mid 7n +4$, for some integer $n$, then $a = 1$ or $a = 13$

Published on 27 Jun 2019 - 19:07

score 2.5k · Answer 4 · 2026-03-26 14:33:59

2.5k

Views

Prove that $a^{2n} -b^{2n}$ is divisible by $a+b$

Published on 26 Mar 2026 - 14:33

score 201 · Answer 5 · 2019-07-01 20:02:42

201

Views

If $p, q$ are primes and $p$ does not divide $n-1$ and $p$ divides $n^q-1$. How to prove that $q|p-1$.

Published on 01 Jul 2019 - 20:02

score 33 · Answer 6 · 2026-03-25 10:58:58

33

Views

Find every $a,b \in \mathbb{C}$ such that dividing $P=3X^{120}+\sqrt{2}X^{19}+aX^{11}+\sqrt{2}X^9+3X^2+b$ by $Q=X^2+1$ has remainder $R=5X+2$

Published on 25 Mar 2026 - 10:58

score 374 · Answer 7 · 2019-07-03 09:43:06

374

Views

Prove that $P(x)-x$ divides $ P(P(P(x))) − x $

Published on 03 Jul 2019 - 9:43

score 2.8k · Answer 8 · 2019-07-08 05:54:18

2.8k

Views

Prove that if $ a\mid b$ and $ a+b$ is odd, then $a$ is odd

Published on 08 Jul 2019 - 5:54

score 502 · Answer 9 · 2019-07-08 11:50:27

502

Views

Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime

Published on 08 Jul 2019 - 11:50

score 138 · Answer 10 · 2019-07-09 13:01:42

138

Views

Solving equation with two unknown degrees

Published on 09 Jul 2019 - 13:01

score 52 · Answer 11 · 2026-03-26 14:35:03

52

Views

If $n \mid (a-1)^k$ then $n \mid(a^{n-1} + a^{n-2} + ...+ a + 1) $ and $n,k,a \in N_{\geq2} $

Published on 26 Mar 2026 - 14:35

score 180 · Answer 12 · 2026-03-26 23:09:59

180

Views

Question about Zeta-distribution regarding divisibility by primes

Published on 26 Mar 2026 - 23:09

score 79 · Answer 13 · 2019-07-10 04:39:32

79

Views

If I Know that $d\mid n+5$ then How Do I Know that $d\mid(n+5)(n-5)$

Published on 10 Jul 2019 - 4:39

score 877 · Answer 14 · 2026-03-28 00:30:59

877

Views

Give two integers $m$ and $n$ such that $n^2$ is a multiple of $m$, $n$ is not a multiple of $m$ and $n > m$

Published on 28 Mar 2026 - 0:30

score 2.1k · Answer 15 · 2026-03-26 17:42:26

2.1k

Views

Is there a way to tell if a number is divisible by 4 if the figure is of 2 digits

Published on 26 Mar 2026 - 17:42

List Question

How can I formally prove that $3\mid 2^n+1\iff n=2m+1,m \in \mathbb N$

Find all natural number $n$ such that $n^2 + 2\mid 2001n + 2$

Prime Numbers. Show that if $a \mid 42n + 37$ and $a \mid 7n +4$, for some integer $n$, then $a = 1$ or $a = 13$

Prove that $a^{2n} -b^{2n}$ is divisible by $a+b$

If $p, q$ are primes and $p$ does not divide $n-1$ and $p$ divides $n^q-1$. How to prove that $q|p-1$.

Find every $a,b \in \mathbb{C}$ such that dividing $P=3X^{120}+\sqrt{2}X^{19}+aX^{11}+\sqrt{2}X^9+3X^2+b$ by $Q=X^2+1$ has remainder $R=5X+2$

Prove that $P(x)-x$ divides $ P(P(P(x))) − x $

Prove that if $ a\mid b$ and $ a+b$ is odd, then $a$ is odd

Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime

Solving equation with two unknown degrees

If $n \mid (a-1)^k$ then $n \mid(a^{n-1} + a^{n-2} + ...+ a + 1) $ and $n,k,a \in N_{\geq2} $

Question about Zeta-distribution regarding divisibility by primes

If I Know that $d\mid n+5$ then How Do I Know that $d\mid(n+5)(n-5)$

Give two integers $m$ and $n$ such that $n^2$ is a multiple of $m$, $n$ is not a multiple of $m$ and $n > m$

Is there a way to tell if a number is divisible by 4 if the figure is of 2 digits

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