Question

Game: two stacks of coins and reducing by divisor of number of coins on the stack

score 547 · Answer 1 · 2026-04-15 21:21:58

547

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Game: two stacks of coins and reducing by divisor of number of coins on the stack

Published on 15 Apr 2026 - 21:21

score 37 · Answer 2 · 2026-04-17 19:59:36

37

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Using properties of congruence only, show that $x^2+7x+4$ is divisible by $3$ whenever $x=1+3k $for any integer $k$.

Published on 17 Apr 2026 - 19:59

score 244 · Answer 3 · 2026-04-15 10:01:56

244

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Are $(2,28)$ and $(5,3207)$ the only solutions $(m,n)\in\mathbb{N}^2$?

Published on 15 Apr 2026 - 10:01

score 77 · Answer 4 · 2026-04-13 14:01:00

77

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Strange condition in a step of Brun's Theorem proof

Published on 13 Apr 2026 - 14:01

score 85 · Answer 5 · 2026-04-16 02:38:56

85

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Prove that $9\vert F_{n+24}$ iff $9\vert F_n$.

Published on 16 Apr 2026 - 2:38

score 88 · Answer 6 · 2026-04-17 22:17:39

88

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why does there exist a unitary matrix U for every symmetric matrix A such that $A=UDU^{\dagger}$ where D is a diagonal matrix?

Published on 17 Apr 2026 - 22:17

score 40 · Answer 7 · 2026-04-16 14:20:43

40

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If $F_n<a<F_{n+1}<b<F_{n+2}$ for $n\ge4$,establish that the sum $a+b$ cannot be a Fibonacci number

Published on 16 Apr 2026 - 14:20

score 87 · Answer 8 · 2026-04-10 13:54:45

87

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Is every even square a value of $\varphi(n)$?

Published on 10 Apr 2026 - 13:54

score 345 · Answer 9 · 2026-04-24 01:13:09

345

Views

Basis of the integer ring of $\mathbb{Q}(\sqrt5)$

Published on 24 Apr 2026 - 1:13

score 156 · Answer 10 · 2026-04-17 00:40:14

156

Views

Find integers $a$ in $[1,2014]$ to get solutions in integers of $x+y=a, \frac{x^2}{x-1}+\frac{y^2}{y-1}=4$

Published on 17 Apr 2026 - 0:40

score 823 · Answer 11 · 2026-04-14 20:35:02

823

Views

Proving that $\{\cos n\mid n\in\mathbb N\}$ is dense in $[-1,1]$

Published on 14 Apr 2026 - 20:35

score 148 · Answer 12 · 2026-04-17 07:06:42

148

Views

Use induction to show that $F_{2n} \equiv n(-1)^{n + 1} \pmod 5 \forall n \ge 1$

Published on 17 Apr 2026 - 7:06

score 52 · Answer 13 · 2026-04-16 20:15:39

52

Views

What is the author trying to say about the Chinese remainder theorem?

Published on 16 Apr 2026 - 20:15

score 470 · Answer 14 · 2026-04-21 05:17:37

470

Views

The Galois group of a specialized polynomial

Published on 21 Apr 2026 - 5:17

score 424 · Answer 15 · 2026-04-12 21:23:42

424

Views

Prove that $\mathbb{Z}^+$ is not compact with the arithmetic progression topology

Published on 12 Apr 2026 - 21:23

List Question

Game: two stacks of coins and reducing by divisor of number of coins on the stack

Using properties of congruence only, show that $x^2+7x+4$ is divisible by $3$ whenever $x=1+3k $for any integer $k$.

Are $(2,28)$ and $(5,3207)$ the only solutions $(m,n)\in\mathbb{N}^2$?

Strange condition in a step of Brun's Theorem proof

Prove that $9\vert F_{n+24}$ iff $9\vert F_n$.

why does there exist a unitary matrix U for every symmetric matrix A such that $A=UDU^{\dagger}$ where D is a diagonal matrix?

If $F_n<a<F_{n+1}<b<F_{n+2}$ for $n\ge4$,establish that the sum $a+b$ cannot be a Fibonacci number

Is every even square a value of $\varphi(n)$?

Basis of the integer ring of $\mathbb{Q}(\sqrt5)$

Find integers $a$ in $[1,2014]$ to get solutions in integers of $x+y=a, \frac{x^2}{x-1}+\frac{y^2}{y-1}=4$

Proving that $\{\cos n\mid n\in\mathbb N\}$ is dense in $[-1,1]$

Use induction to show that $F_{2n} \equiv n(-1)^{n + 1} \pmod 5 \forall n \ge 1$

What is the author trying to say about the Chinese remainder theorem?

The Galois group of a specialized polynomial

Prove that $\mathbb{Z}^+$ is not compact with the arithmetic progression topology

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