Question

Proving that $6^{2n+1} + 1$ is divisible by $7$ for $n\geq 1$ by induction

score 561 · Answer 1 · 2015-05-27 15:18:41

561

Views

Proving that $6^{2n+1} + 1$ is divisible by $7$ for $n\geq 1$ by induction

Published on 27 May 2015 - 15:18

score 953 · Answer 2 · 2026-04-10 18:27:30

953

Views

Bezout Coefficient for polynomials in sage?

Published on 10 Apr 2026 - 18:27

score 183 · Answer 3 · 2015-05-28 05:04:34

183

Views

Sum of $m\leq 300$ such that if $2013m$ divides $n^{n}-1$, then $2013m$ also divides $n-1$

Published on 28 May 2015 - 5:04

score 538 · Answer 4 · 2026-04-02 21:39:29

538

Views

$\gcd(N, a)=\gcd(N, N-a)$ for positive integers $N$ and $a$?

Published on 02 Apr 2026 - 21:39

score 56.4k · Answer 5 · 2026-04-10 23:47:43

56.4k

Views

What does "$x$ divides $y$" mean?

Published on 10 Apr 2026 - 23:47

score 1.2k · Answer 6 · 2015-05-29 18:59:43

1.2k

Views

Find the greatest positive integer $x$ such that $23^{6+x}$ divides $2000!$

Published on 29 May 2015 - 18:59

score 246 · Answer 7 · 2015-05-30 14:35:09

246

Views

Prove that if $p$ is prime greater than $3$ ,then: $p^2+2015$ is multiple of $24$?

Published on 30 May 2015 - 14:35

score 258 · Answer 8 · 2026-04-11 15:20:06

258

Views

Prove that there exist $2015$ consecutive abundant numbers

Published on 11 Apr 2026 - 15:20

score 84 · Answer 9 · 2015-05-31 19:02:24

84

Views

Find all $n \in \mathbb{Z}$ such that $ k = \frac{1+4n}{5}, \qquad (k \in \mathbb{Z} )$

Published on 31 May 2015 - 19:02

score 1.6k · Answer 10 · 2026-04-12 04:47:17

1.6k

Views

Find the $\gcd(81,237)$ and express it as a linear combination of $81$ and $237.$

Published on 12 Apr 2026 - 4:47

score 590 · Answer 11 · 2015-06-03 18:48:44

590

Views

Find all positive integers solutions such that $3^k$ divides $2^n-1$

Published on 03 Jun 2015 - 18:48

score 15.8k · Answer 12 · 2026-04-11 07:43:01

15.8k

Views

Greatest common Divisor of negative numbers

Published on 11 Apr 2026 - 7:43

score 748 · Answer 13 · 2026-04-10 17:43:23

748

Views

Induction proof, divisibility

Published on 10 Apr 2026 - 17:43

score 1.2k · Answer 14 · 2026-03-27 18:34:41

1.2k

Views

Why does the largest $x$ such that $a$, $b$ divided by $x$ leave the same remainder equal $a-b$?

Published on 27 Mar 2026 - 18:34

score 407 · Answer 15 · 2026-04-11 11:10:00

407

Views

Solving a Diophantine equation with LTE

Published on 11 Apr 2026 - 11:10

List Question

Proving that $6^{2n+1} + 1$ is divisible by $7$ for $n\geq 1$ by induction

Bezout Coefficient for polynomials in sage?

Sum of $m\leq 300$ such that if $2013m$ divides $n^{n}-1$, then $2013m$ also divides $n-1$

$\gcd(N, a)=\gcd(N, N-a)$ for positive integers $N$ and $a$?

What does "$x$ divides $y$" mean?

Find the greatest positive integer $x$ such that $23^{6+x}$ divides $2000!$

Prove that if $p$ is prime greater than $3$ ,then: $p^2+2015$ is multiple of $24$?

Prove that there exist $2015$ consecutive abundant numbers

Find all $n \in \mathbb{Z}$ such that $ k = \frac{1+4n}{5}, \qquad (k \in \mathbb{Z} )$

Find the $\gcd(81,237)$ and express it as a linear combination of $81$ and $237.$

Find all positive integers solutions such that $3^k$ divides $2^n-1$

Greatest common Divisor of negative numbers

Induction proof, divisibility

Why does the largest $x$ such that $a$, $b$ divided by $x$ leave the same remainder equal $a-b$?

Solving a Diophantine equation with LTE

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