Question

With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$

score 696 · Answer 1 · 2026-04-15 23:01:15

696

Views

With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$

Published on 15 Apr 2026 - 23:01

score 53 · Answer 2 · 2026-04-17 05:10:49

53

Views

Let $n ∈ ℤ⁺$ with $n > 1$. Prove: If $a ≡ 1$ (mod $n²$), then $a^n ≡ 1$ (mod $n³$)

Published on 17 Apr 2026 - 5:10

score 176 · Answer 3 · 2026-04-14 00:36:32

176

Views

Finding the maximium product of the cardinalites of the elements of the partitions of a finite set.

Published on 14 Apr 2026 - 0:36

score 88 · Answer 4 · 2026-04-14 20:49:07

88

Views

What’s the relation between definability of a class of structure and the completeness of a set of axioms?

Published on 14 Apr 2026 - 20:49

score 236 · Answer 5 · 2026-05-05 02:03:55

236

Views

When are $a+b$ and $ab$ palindromic for integers $a,b$?

Published on 05 May 2026 - 2:03

score 146 · Answer 6 · 2026-04-15 16:46:00

146

Views

Let $a\mid bc $ then prove or disprove $a\mid (a,b)c$

Published on 15 Apr 2026 - 16:46

score 193 · Answer 7 · 2026-04-16 12:24:52

193

Views

What is the least prime factor of $n^i \cdot m^j$, for prime numbers $n, m$ such that $n < m$?

Published on 16 Apr 2026 - 12:24

score 83 · Answer 8 · 2026-04-16 11:39:16

83

Views

Numbers $m$ such that $\sqrt{-1}$ mod $m$ exists

Published on 16 Apr 2026 - 11:39

score 161 · Answer 9 · 2026-04-17 14:18:40

161

Views

$(2n-1)(2n-3)\cdots 3\cdot1 = \frac{(2n)!}{2^nn!}$

Published on 17 Apr 2026 - 14:18

score 207 · Answer 10 · 2026-04-17 12:30:17

207

Views

Finding $1^1+2^2+\cdots+99^{99}\pmod3$

Published on 17 Apr 2026 - 12:30

score 87 · Answer 11 · 2026-04-13 23:45:55

87

Views

Mersenne numbers $M_{p-1}$ divisible by $p^2$

Published on 13 Apr 2026 - 23:45

score 695 · Answer 12 · 2026-04-13 21:02:48

695

Views

$ax\equiv b\pmod{\! n}$ has a unique solution if $\gcd(a,n) = 1$

Published on 13 Apr 2026 - 21:02

score 260 · Answer 13 · 2026-05-03 05:53:03

260

Views

Compressing the primes using simple addition?

Published on 03 May 2026 - 5:53

score 344 · Answer 14 · 2026-04-15 23:19:57

Suppose that $a$ and $b$ are relatively prime natural numbers such that $ab$ is a perfect square. Show that $a$ and $b$ are each perfect squares.

score 293 · Answer 15 · 2026-04-13 11:44:18

293

Views

Integers which are squared norm of 2 by 2 integer matrices

Published on 13 Apr 2026 - 11:44

List Question

With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$

Let $n ∈ ℤ⁺$ with $n > 1$. Prove: If $a ≡ 1$ (mod $n²$), then $a^n ≡ 1$ (mod $n³$)

Finding the maximium product of the cardinalites of the elements of the partitions of a finite set.

What’s the relation between definability of a class of structure and the completeness of a set of axioms?

When are $a+b$ and $ab$ palindromic for integers $a,b$?

Let $a\mid bc $ then prove or disprove $a\mid (a,b)c$

What is the least prime factor of $n^i \cdot m^j$, for prime numbers $n, m$ such that $n < m$?

Numbers $m$ such that $\sqrt{-1}$ mod $m$ exists

$(2n-1)(2n-3)\cdots 3\cdot1 = \frac{(2n)!}{2^nn!}$

Finding $1^1+2^2+\cdots+99^{99}\pmod3$

Mersenne numbers $M_{p-1}$ divisible by $p^2$

$ax\equiv b\pmod{\! n}$ has a unique solution if $\gcd(a,n) = 1$

Compressing the primes using simple addition?

Suppose that $a$ and $b$ are relatively prime natural numbers such that $ab$ is a perfect square. Show that $a$ and $b$ are each perfect squares.

Integers which are squared norm of 2 by 2 integer matrices

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