Question

What are the Legendre symbols $\left(\frac{10}{31}\right)$ and $\left(\frac{-15}{43}\right)$?

score 405 · Answer 1 · 2026-05-10 12:55:17

405

Views

What are the Legendre symbols $\left(\frac{10}{31}\right)$ and $\left(\frac{-15}{43}\right)$?

Published on 10 May 2026 - 12:55

score 755 · Answer 2 · 2026-04-15 17:11:02

755

Views

Find the least nonnegative residue of: $42^{173} modulo 13$

Published on 15 Apr 2026 - 17:11

score 122 · Answer 3 · 2026-04-10 20:00:10

122

Views

Elementary number theory proof involving multiplied gcd's

Published on 10 Apr 2026 - 20:00

score 164 · Answer 4 · 2026-04-16 11:49:41

164

Views

Proof that a finite series expansion of $f(X)$ at $\alpha$ exists iff $Q(X)$ is a power of $(X-\alpha)$, in $f(X)=\frac{P(X)}{Q(X)}$

Published on 16 Apr 2026 - 11:49

score 75 · Answer 5 · 2026-04-16 16:49:01

75

Views

If $m, n>0$ and $\gcd(m, n) =d$, then $\gcd(a^m-1, a^n-1) =a^d-1$.

Published on 16 Apr 2026 - 16:49

score 328 · Answer 6 · 2026-04-14 00:22:10

328

Views

The general proposition of Fermat

Published on 14 Apr 2026 - 0:22

score 48 · Answer 7 · 2026-04-12 18:48:42

48

Views

Basic modular arithmetic question

Published on 12 Apr 2026 - 18:48

score 81 · Answer 8 · 2026-04-25 03:19:17

Let $a<b<c$, where $a$ is a positive integer and $b$ and $c$ are odd primes. Prove that if $a \mid (3b+2c)$ and $a \mid (2b+3c)$, then $a=1$ or $5$.

score 280 · Answer 9 · 2026-05-11 05:45:04

280

Views

Prove that if $a, b, c \in \mathbb{Z^+}$ and $a^2+b^2=c^2$ then ${1\over2}(c-a)(c-b)$ is a perfect square.

Published on 11 May 2026 - 5:45

score 120 · Answer 10 · 2026-04-14 03:30:19

120

Views

An elementary problem of proving congruences in a statement about absolute Galois group for $\mathbb{F}_{p}.$

Published on 14 Apr 2026 - 3:30

score 101 · Answer 11 · 2026-04-14 04:30:40

101

Views

Problem parallel to Goldbach Conjecture

Published on 14 Apr 2026 - 4:30

score 299 · Answer 12 · 2026-04-09 03:55:49

299

Views

Prove that for all $n$ $\gcd(n, x_n)=1$, given $x_{n+1}=2(x_n)^2-1$ and $x_1=2$

Published on 09 Apr 2026 - 3:55

score 105 · Answer 13 · 2026-04-15 06:24:45

105

Views

Solving the Diophantine equation $y^2 = x^4+x+ 2$ for $x,y \in \mathbb{Z}$

Published on 15 Apr 2026 - 6:24

score 137 · Answer 14 · 2026-04-16 14:10:07

137

Views

Showing that the Diophantine equation $3x^2 + 6y^6 + 1 = 8xy^3$ has no solutions $x,y \in \mathbb{Q}$

Published on 16 Apr 2026 - 14:10

score 266 · Answer 15 · 2026-05-10 15:01:28

266

Views

Solving the Diophantine equation $y^3 = 4x^2+4x+ 5$ for $x,y \in \mathbb{Z}$

Published on 10 May 2026 - 15:01

List Question

What are the Legendre symbols $\left(\frac{10}{31}\right)$ and $\left(\frac{-15}{43}\right)$?

Find the least nonnegative residue of: $42^{173} modulo 13$

Elementary number theory proof involving multiplied gcd's

Proof that a finite series expansion of $f(X)$ at $\alpha$ exists iff $Q(X)$ is a power of $(X-\alpha)$, in $f(X)=\frac{P(X)}{Q(X)}$

If $m, n>0$ and $\gcd(m, n) =d$, then $\gcd(a^m-1, a^n-1) =a^d-1$.

The general proposition of Fermat

Basic modular arithmetic question

Let $a<b<c$, where $a$ is a positive integer and $b$ and $c$ are odd primes. Prove that if $a \mid (3b+2c)$ and $a \mid (2b+3c)$, then $a=1$ or $5$.

Prove that if $a, b, c \in \mathbb{Z^+}$ and $a^2+b^2=c^2$ then ${1\over2}(c-a)(c-b)$ is a perfect square.

An elementary problem of proving congruences in a statement about absolute Galois group for $\mathbb{F}_{p}.$

Problem parallel to Goldbach Conjecture

Prove that for all $n$ $\gcd(n, x_n)=1$, given $x_{n+1}=2(x_n)^2-1$ and $x_1=2$

Solving the Diophantine equation $y^2 = x^4+x+ 2$ for $x,y \in \mathbb{Z}$

Showing that the Diophantine equation $3x^2 + 6y^6 + 1 = 8xy^3$ has no solutions $x,y \in \mathbb{Q}$

Solving the Diophantine equation $y^3 = 4x^2+4x+ 5$ for $x,y \in \mathbb{Z}$

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