Question

How many positive integer solution pairs $(x, y)$ are there for the equation $y^2 = \frac{(x^5 - 1)}{(x-1)} $, $x\neq 1$?

score 133 · Answer 1 · 2026-04-15 14:28:58

133

Views

How many positive integer solution pairs $(x, y)$ are there for the equation $y^2 = \frac{(x^5 - 1)}{(x-1)} $, $x\neq 1$?

Published on 15 Apr 2026 - 14:28

score 181 · Answer 2 · 2026-04-11 20:54:51

181

Views

Maximum of least common multiple of numbers whose sum is fixed

Published on 11 Apr 2026 - 20:54

score 65 · Answer 3 · 2026-04-14 00:16:11

65

Views

If $m$ is odd and not prime

Published on 14 Apr 2026 - 0:16

score 67 · Answer 4 · 2026-04-15 03:18:12

67

Views

Is $a$ or $b \equiv 0 \pmod{5}$ if $a^2-b^2 \equiv 0 \pmod{5}$?

Published on 15 Apr 2026 - 3:18

score 152 · Answer 5 · 2026-04-14 13:57:11

152

Views

Relatively prime numbers and probability.

Published on 14 Apr 2026 - 13:57

score 95 · Answer 6 · 2026-05-10 21:57:36

95

Views

Is $\Bbb Q[\alpha]$ a field ? where, $\alpha \in \Bbb C$ such that $\alpha + \pi = {\pi}^2 \alpha $

Published on 10 May 2026 - 21:57

score 100 · Answer 7 · 2026-04-15 20:01:18

100

Views

Prove that $\sum\limits_{k=1}^n\lfloor n/k\rfloor+\lfloor \sqrt{n} \rfloor$ is even.

Published on 15 Apr 2026 - 20:01

score 127 · Answer 8 · 2026-04-16 15:59:48

127

Views

Find remainder when $8^{13^{48}}$ divided by 1000

Published on 16 Apr 2026 - 15:59

score 412 · Answer 9 · 2026-04-15 22:56:46

412

Views

Let $X =\{n^3 + 3n^2 +3n | n>0\}$ and $Y = \{ n^3 -1 | n>0\}.$ Prove that $X =Y$.

Published on 15 Apr 2026 - 22:56

score 212 · Answer 10 · 2026-04-14 20:04:10

212

Views

AMC 2000, Problem 16

Published on 14 Apr 2026 - 20:04

score 83 · Answer 11 · 2026-05-04 14:55:38

83

Views

Prove that for a given prime $p$ and each $0 < r < p-1$, there exists a $q$ such that $rq \equiv 1 \bmod p$

Published on 04 May 2026 - 14:55

score 210 · Answer 12 · 2026-04-16 05:28:55

210

Views

If $n,m \in \mathbb{N}$ then there are $c,d$ such that $cd = (m,n)$, $(c,d) = 1$ and $(m/c,n/d) = 1$.

Published on 16 Apr 2026 - 5:28

score 513 · Answer 13 · 2026-04-16 18:18:56

513

Views

When does the first repetition in $\;\lfloor x\rfloor, \lfloor x/2 \rfloor, \lfloor x/3\rfloor, \lfloor x/4\rfloor, \dots\;$ appear?

Published on 16 Apr 2026 - 18:18

score 169 · Answer 14 · 2026-05-14 06:18:28

169

Views

Nested powers remainder problem.

Published on 14 May 2026 - 6:18

score 977 · Answer 15 · 2026-04-17 11:07:09

977

Views

show that no number in the sequence $2, 22, 222, 2222, \ldots$ is a perfect square

Published on 17 Apr 2026 - 11:07

List Question

How many positive integer solution pairs $(x, y)$ are there for the equation $y^2 = \frac{(x^5 - 1)}{(x-1)} $, $x\neq 1$?

Maximum of least common multiple of numbers whose sum is fixed

If $m$ is odd and not prime

Is $a$ or $b \equiv 0 \pmod{5}$ if $a^2-b^2 \equiv 0 \pmod{5}$?

Relatively prime numbers and probability.

Is $\Bbb Q[\alpha]$ a field ? where, $\alpha \in \Bbb C$ such that $\alpha + \pi = {\pi}^2 \alpha $

Prove that $\sum\limits_{k=1}^n\lfloor n/k\rfloor+\lfloor \sqrt{n} \rfloor$ is even.

Find remainder when $8^{13^{48}}$ divided by 1000

Let $X =\{n^3 + 3n^2 +3n | n>0\}$ and $Y = \{ n^3 -1 | n>0\}.$ Prove that $X =Y$.

AMC 2000, Problem 16

Prove that for a given prime $p$ and each $0 < r < p-1$, there exists a $q$ such that $rq \equiv 1 \bmod p$

If $n,m \in \mathbb{N}$ then there are $c,d$ such that $cd = (m,n)$, $(c,d) = 1$ and $(m/c,n/d) = 1$.

When does the first repetition in $\;\lfloor x\rfloor, \lfloor x/2 \rfloor, \lfloor x/3\rfloor, \lfloor x/4\rfloor, \dots\;$ appear?

Nested powers remainder problem.

show that no number in the sequence $2, 22, 222, 2222, \ldots$ is a perfect square

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