Question

What are the integral solutions of $239x-111y=1$

score 122 · Answer 1 · 2026-04-11 22:19:12

122

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What are the integral solutions of $239x-111y=1$

Published on 11 Apr 2026 - 22:19

score 97 · Answer 2 · 2026-04-17 14:36:46

97

Views

Prove that if $m, n, d\in\mathbb{Z^+}$ and $d \mid m^2n+1, d \mid mn^2+1$ then $d \mid m^3+1, d \mid n^3+1$

Published on 17 Apr 2026 - 14:36

score 52 · Answer 3 · 2026-04-16 09:55:19

52

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Any other quick way to find the remainder?

Published on 16 Apr 2026 - 9:55

score 102 · Answer 4 · 2026-05-10 22:02:43

102

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$N \in \mathbb{N}$ is not a square, show that the continued fraction expansion of $\sqrt N/\lfloor\sqrt N\rfloor$ is $[1,\overline{a_1,a_2,\dots,2}]$

Published on 10 May 2026 - 22:02

score 124 · Answer 5 · 2026-04-15 13:24:35

124

Views

Find $7^{2018}-1 \bmod 5$ using Fermat's Little Theorem

Published on 15 Apr 2026 - 13:24

score 37 · Answer 6 · 2026-04-09 16:58:44

37

Views

Diophantine Equations (another)

Published on 09 Apr 2026 - 16:58

score 2.1k · Answer 7 · 2026-04-14 07:37:19

2.1k

Views

Sum of two co-prime integers

Published on 14 Apr 2026 - 7:37

score 68 · Answer 8 · 2026-04-09 11:23:16

68

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If $1\le a_1<\cdots<a_n\le 2n$ satisfy $\operatorname{lcm}(a_i,a_j)>2n$ for $i\ne j$, is $a_i>\frac{2n}{3}$ for all $i$?

Published on 09 Apr 2026 - 11:23

score 80 · Answer 9 · 2026-04-15 14:38:04

80

Views

Every odd divisor is $\equiv 1\bmod 3$

Published on 15 Apr 2026 - 14:38

score 197 · Answer 10 · 2026-04-16 06:15:02

197

Views

Finding a formula for the number of $0$-$1$ sequences of length $n$ having a $0$ in any consecutive $m$ digits

Published on 16 Apr 2026 - 6:15

score 410 · Answer 11 · 2026-04-12 03:48:54

410

Views

How did Euler show that number is idoneal?

Published on 12 Apr 2026 - 3:48

score 71 · Answer 12 · 2026-04-17 02:30:16

71

Views

Let $x \in \mathbb{N}$ and let $p$ be a prime divisor of $x^4+x^3+x^2+x+1$, prove that $p = 5$ or $p \equiv 1 \mod{5}$

Published on 17 Apr 2026 - 2:30

score 306 · Answer 13 · 2026-04-14 06:00:36

306

Views

Disprove that if $n$ is an odd positive integer greater than $1$ then $2^n-1$ is prime.

Published on 14 Apr 2026 - 6:00

score 73 · Answer 14 · 2026-04-16 17:31:15

73

Views

$ \frac{m^a}{2} + \frac{m}{2}-1 $ is not prime, $m \geq 4$ even integer, $ a\in \mathbb{Z}, a \geq 2 $

Published on 16 Apr 2026 - 17:31

score 151 · Answer 15 · 2026-04-17 01:18:04

151

Views

Determine number of all $\left\{P,Q,R,k \right\}$, such that $P_{(2k)}-Q_{(k)}=(R_{(k)})^2$

Published on 17 Apr 2026 - 1:18

List Question

What are the integral solutions of $239x-111y=1$

Prove that if $m, n, d\in\mathbb{Z^+}$ and $d \mid m^2n+1, d \mid mn^2+1$ then $d \mid m^3+1, d \mid n^3+1$

Any other quick way to find the remainder?

$N \in \mathbb{N}$ is not a square, show that the continued fraction expansion of $\sqrt N/\lfloor\sqrt N\rfloor$ is $[1,\overline{a_1,a_2,\dots,2}]$

Find $7^{2018}-1 \bmod 5$ using Fermat's Little Theorem

Diophantine Equations (another)

Sum of two co-prime integers

If $1\le a_1<\cdots<a_n\le 2n$ satisfy $\operatorname{lcm}(a_i,a_j)>2n$ for $i\ne j$, is $a_i>\frac{2n}{3}$ for all $i$?

Every odd divisor is $\equiv 1\bmod 3$

Finding a formula for the number of $0$-$1$ sequences of length $n$ having a $0$ in any consecutive $m$ digits

How did Euler show that number is idoneal?

Let $x \in \mathbb{N}$ and let $p$ be a prime divisor of $x^4+x^3+x^2+x+1$, prove that $p = 5$ or $p \equiv 1 \mod{5}$

Disprove that if $n$ is an odd positive integer greater than $1$ then $2^n-1$ is prime.

$ \frac{m^a}{2} + \frac{m}{2}-1 $ is not prime, $m \geq 4$ even integer, $ a\in \mathbb{Z}, a \geq 2 $

Determine number of all $\left\{P,Q,R,k \right\}$, such that $P_{(2k)}-Q_{(k)}=(R_{(k)})^2$

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