Question

Prove that $\gcd\left(n^{a}+1, n^{b}+1\right)\mid (n^{\gcd(a, b)}+1)$

score 577 · Answer 1 · 2026-03-26 11:17:30

577

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Prove that $\gcd\left(n^{a}+1, n^{b}+1\right)\mid (n^{\gcd(a, b)}+1)$

Published on 26 Mar 2026 - 11:17

score 75 · Answer 2 · 2026-03-30 15:05:15

75

Views

Unique solution of the equation $\prod_{i=1}^m(a_i+1)\prod_{i=1}^n(b_i)=\prod_{i=1}^m(a_i)\prod_{i=1}^n(b_i+1)$

Published on 30 Mar 2026 - 15:05

score 262 · Answer 3 · 2020-05-24 02:19:05

262

Views

How to draw hasse diagram - divisibility - R and inverse R

Published on 24 May 2020 - 2:19

score 121 · Answer 4 · 2026-04-01 04:15:33

121

Views

Total ordering - Partially ordered set

Published on 01 Apr 2026 - 4:15

score 95 · Answer 5 · 2020-05-25 13:43:19

95

Views

Find solutions of $m=\frac{n^2}{(n-m-1)\lambda+n}$ where $n,m,\lambda$ are postive integers,$1\le\lambda \le n-1$ and $m\mid n$.

Published on 25 May 2020 - 13:43

score 734 · Answer 6 · 2026-02-23 08:34:00

734

Views

Divisibility of $a_{24}$ by 7. ($a_n=\underbrace{999\cdots9 }_{n \text{ times}})$

Published on 23 Feb 2026 - 8:34

score 41 · Answer 7 · 2020-05-26 13:44:16

41

Views

How many solutions are there to the congruence

Published on 26 May 2020 - 13:44

score 94 · Answer 8 · 2020-05-26 14:32:50

94

Views

Use Fermat's Little Theorem

Published on 26 May 2020 - 14:32

score 200 · Answer 9 · 2026-03-27 20:12:05

200

Views

Parity of Euler's totient function

Published on 27 Mar 2026 - 20:12

score 104 · Answer 10 · 2020-05-27 10:08:29

104

Views

On composite numbers $n$ such that $n^2\equiv 1\text{ mod }\psi(n)$, where $\psi(n)$ denotes the Dedekind psi function

Published on 27 May 2020 - 10:08

score 223 · Answer 11 · 2026-03-29 12:05:37

223

Views

Equations involving particular values of the Dedekind psi function and powers of the kernel function

Published on 29 Mar 2026 - 12:05

score 353 · Answer 12 · 2026-04-02 07:04:40

353

Views

How to choose a special modulus to show that $6n^3 +3 = m^6$ has no solutions in the integers

Published on 02 Apr 2026 - 7:04

score 70 · Answer 13 · 2026-04-02 07:09:07

70

Views

Iran Mathematics Olympiad Problem

Published on 02 Apr 2026 - 7:09

score 113 · Answer 14 · 2020-05-28 13:41:05

113

Views

Number of ordered Pairs satisfying $4^m-3^n=1$

Published on 28 May 2020 - 13:41

score 153 · Answer 15 · 2026-03-30 10:13:59

153

Views

$P,R \neq 0$ are polynomials with rational coefficients. Show that there exists a polynomial $Q$ such that $P(X) | Q(R(X))$

Published on 30 Mar 2026 - 10:13

List Question

Prove that $\gcd\left(n^{a}+1, n^{b}+1\right)\mid (n^{\gcd(a, b)}+1)$

Unique solution of the equation $\prod_{i=1}^m(a_i+1)\prod_{i=1}^n(b_i)=\prod_{i=1}^m(a_i)\prod_{i=1}^n(b_i+1)$

How to draw hasse diagram - divisibility - R and inverse R

Total ordering - Partially ordered set

Find solutions of $m=\frac{n^2}{(n-m-1)\lambda+n}$ where $n,m,\lambda$ are postive integers,$1\le\lambda \le n-1$ and $m\mid n$.

Divisibility of $a_{24}$ by 7. ($a_n=\underbrace{999\cdots9 }_{n \text{ times}})$

How many solutions are there to the congruence

Use Fermat's Little Theorem

Parity of Euler's totient function

On composite numbers $n$ such that $n^2\equiv 1\text{ mod }\psi(n)$, where $\psi(n)$ denotes the Dedekind psi function

Equations involving particular values of the Dedekind psi function and powers of the kernel function

How to choose a special modulus to show that $6n^3 +3 = m^6$ has no solutions in the integers

Iran Mathematics Olympiad Problem

Number of ordered Pairs satisfying $4^m-3^n=1$

$P,R \neq 0$ are polynomials with rational coefficients. Show that there exists a polynomial $Q$ such that $P(X) | Q(R(X))$

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