Question

Proof that $\sqrt[3]{17}$ is irrational

score 781 · Answer 1 · 2026-04-13 21:26:38

781

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Proof that $\sqrt[3]{17}$ is irrational

Published on 13 Apr 2026 - 21:26

score 188 · Answer 2 · 2026-04-17 03:16:52

188

Views

If $a$ is rational and $18a$ and $25a$ integers then so is $a$. Same for any coprime multipliers. Denominators closed under gcd.

Published on 17 Apr 2026 - 3:16

score 60 · Answer 3 · 2026-04-13 00:27:15

60

Views

Proof verification that $\gcd(a,b)=\gcd(a, b- k \cdot a )$

Published on 13 Apr 2026 - 0:27

score 340 · Answer 4 · 2026-04-13 12:09:29

340

Views

Prove that $\gcd(a,0)=|a|$

Published on 13 Apr 2026 - 12:09

score 899 · Answer 5 · 2026-04-24 14:40:53

899

Views

Prove: $2n^{2} + 3n$ is even if and only if $n^{3} - 4$ is even.

Published on 24 Apr 2026 - 14:40

score 114 · Answer 6 · 2026-04-17 04:52:26

114

Views

the sum of the convolutions with themselves of the coprimes of composite $n$

Published on 17 Apr 2026 - 4:52

score 97 · Answer 7 · 2026-04-15 10:31:45

97

Views

Difference between a non-increasing number and it's mirror (digit reversal)

Published on 15 Apr 2026 - 10:31

score 224 · Answer 8 · 2026-04-15 02:34:41

224

Views

Competition Diophantine Equation

Published on 15 Apr 2026 - 2:34

score 99 · Answer 9 · 2026-04-13 06:38:53

99

Views

For all non-zero positive integers $a, b, c$ prove $[a, b, c] = \frac{abc (a, b, c)}{(a, b) (b, c) (c, a)}$

Published on 13 Apr 2026 - 6:38

score 1.4k · Answer 10 · 2026-04-13 19:44:00

1.4k

Views

How many ways can a number $n>2$ be expressed as the difference of two squares?

Published on 13 Apr 2026 - 19:44

score 148 · Answer 11 · 2026-04-14 14:47:10

148

Views

Proving the Sylvester-Schur Theorem

Published on 14 Apr 2026 - 14:47

score 222 · Answer 12 · 2026-04-14 01:54:05

222

Views

How does one get all substructures of the Integers?

Published on 14 Apr 2026 - 1:54

score 410 · Answer 13 · 2026-04-16 00:23:40

410

Views

A number is triangular if and only if it is of the form $\frac{(n)(n+1)}{2}$

Published on 16 Apr 2026 - 0:23

score 52 · Answer 14 · 2026-04-16 14:51:42

52

Views

Let $q$ be an integer $\geq 3$. Prove that there are infinitely many primes $p$ with $p\not\equiv 1 \mod q$.

Published on 16 Apr 2026 - 14:51

score 2.4k · Answer 15 · 2026-04-14 17:58:03

2.4k

Views

Show, for $F(n)$ the $n$-th Fibonacci number, that $\gcd(F(n),F(n-1))=1$, and that the Euclidean algorithm calculation takes $n-2$ steps

Published on 14 Apr 2026 - 17:58

List Question

Proof that $\sqrt[3]{17}$ is irrational

If $a$ is rational and $18a$ and $25a$ integers then so is $a$. Same for any coprime multipliers. Denominators closed under gcd.

Proof verification that $\gcd(a,b)=\gcd(a, b- k \cdot a )$

Prove that $\gcd(a,0)=|a|$

Prove: $2n^{2} + 3n$ is even if and only if $n^{3} - 4$ is even.

the sum of the convolutions with themselves of the coprimes of composite $n$

Difference between a non-increasing number and it's mirror (digit reversal)

Competition Diophantine Equation

For all non-zero positive integers $a, b, c$ prove $[a, b, c] = \frac{abc (a, b, c)}{(a, b) (b, c) (c, a)}$

How many ways can a number $n>2$ be expressed as the difference of two squares?

Proving the Sylvester-Schur Theorem

How does one get all substructures of the Integers?

A number is triangular if and only if it is of the form $\frac{(n)(n+1)}{2}$

Let $q$ be an integer $\geq 3$. Prove that there are infinitely many primes $p$ with $p\not\equiv 1 \mod q$.

Show, for $F(n)$ the $n$-th Fibonacci number, that $\gcd(F(n),F(n-1))=1$, and that the Euclidean algorithm calculation takes $n-2$ steps

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