Question

Maximizing $\sum\left(\lfloor \frac{n_i}{2} \rfloor+1\right)$ for a partition $\{n_i\}$ of $N$

score 87 · Answer 1 · 2026-04-03 07:32:33

87

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Maximizing $\sum\left(\lfloor \frac{n_i}{2} \rfloor+1\right)$ for a partition $\{n_i\}$ of $N$

Published on 03 Apr 2026 - 7:32

score 131 · Answer 2 · 2026-04-04 06:24:45

131

Views

prove that there is no non zero solution to $a^3+b^3=c^3$

Published on 04 Apr 2026 - 6:24

score 602 · Answer 3 · 2026-04-04 09:39:31

602

Views

Proof of divisibility by three test

Published on 04 Apr 2026 - 9:39

score 40 · Answer 4 · 2026-04-04 13:13:25

40

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intuition for basic inequality involving exponentials

Published on 04 Apr 2026 - 13:13

score 393 · Answer 5 · 2026-04-04 10:34:46

393

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show that if $a$ and $b$ are relatively prime integers then $gcd(a+kb, b+ka)$ divides $k^2-1$

Published on 04 Apr 2026 - 10:34

score 541 · Answer 6 · 2026-04-04 03:59:16

541

Views

ELEMENTARY PROOF: Prove $a^2b^2(a^2-b^2)$ is divisible by $12$.

Published on 04 Apr 2026 - 3:59

score 881 · Answer 7 · 2026-04-04 16:04:39

881

Views

Let $n$ be a 6-digit number, perfect square and perfect cube. If $n-6$ is not even or a multiple of 3, find $n$

Published on 04 Apr 2026 - 16:04

score 56 · Answer 8 · 2026-04-05 09:46:20

56

Views

Unable to understand a statement for congruences.

Published on 05 Apr 2026 - 9:46

score 6.7k · Answer 9 · 2026-04-04 01:31:56

6.7k

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Prove that the nth prime number $p_n$ satisfies $p_n\leq 2^{2n-1}$

Published on 04 Apr 2026 - 1:31

score 57 · Answer 10 · 2026-04-03 20:15:06

57

Views

Finding subsequences $\mathbf{c}$ of $\mathbf{b}$ such that $\mathbf{a}\cdot\mathbf{c} \equiv 0\bmod t$ for fixed sequences $\mathbb{a},\mathbb{b}$

Published on 03 Apr 2026 - 20:15

score 30 · Answer 11 · 2026-04-03 19:32:48

30

Views

Non-constructive proof for a prime $p, \forall k \in \mathbb{Z+}, a\equiv b\pmod {p^k}\implies a\equiv b\pmod p.$

Published on 03 Apr 2026 - 19:32

score 487 · Answer 12 · 2026-04-06 17:46:20

487

Views

Using factorization to solve modulo arithmetic involving big numbers.

Published on 06 Apr 2026 - 17:46

score 237 · Answer 13 · 2026-04-04 13:36:22

237

Views

Compositeness test for repunits in base $-3$

Published on 04 Apr 2026 - 13:36

score 642 · Answer 14 · 2026-04-03 16:55:32

642

Views

show if n=4k+3 is a prime and a2+b2≡0(modn) , then

Published on 03 Apr 2026 - 16:55

score 120 · Answer 15 · 2026-04-04 12:29:27

120

Views

Prove for prime $p, \forall l \in \mathbb Z^+, a\equiv b\pmod {p}\nrightarrow a\equiv b\pmod {p^l}.$

Published on 04 Apr 2026 - 12:29

List Question

Maximizing $\sum\left(\lfloor \frac{n_i}{2} \rfloor+1\right)$ for a partition $\{n_i\}$ of $N$

prove that there is no non zero solution to $a^3+b^3=c^3$

Proof of divisibility by three test

intuition for basic inequality involving exponentials

show that if $a$ and $b$ are relatively prime integers then $gcd(a+kb, b+ka)$ divides $k^2-1$

ELEMENTARY PROOF: Prove $a^2b^2(a^2-b^2)$ is divisible by $12$.

Let $n$ be a 6-digit number, perfect square and perfect cube. If $n-6$ is not even or a multiple of 3, find $n$

Unable to understand a statement for congruences.

Prove that the nth prime number $p_n$ satisfies $p_n\leq 2^{2n-1}$

Finding subsequences $\mathbf{c}$ of $\mathbf{b}$ such that $\mathbf{a}\cdot\mathbf{c} \equiv 0\bmod t$ for fixed sequences $\mathbb{a},\mathbb{b}$

Non-constructive proof for a prime $p, \forall k \in \mathbb{Z+}, a\equiv b\pmod {p^k}\implies a\equiv b\pmod p.$

Using factorization to solve modulo arithmetic involving big numbers.

Compositeness test for repunits in base $-3$

show if n=4k+3 is a prime and a2+b2≡0(modn) , then

Prove for prime $p, \forall l \in \mathbb Z^+, a\equiv b\pmod {p}\nrightarrow a\equiv b\pmod {p^l}.$

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