Question

Prove the equation $\left(2x^2+1\right)\left(2y^2+1\right)=4z^2+1$ has no solution in the positive integers

score 541 · Answer 1 · 2018-07-10 11:53:19

541

Views

Prove the equation $\left(2x^2+1\right)\left(2y^2+1\right)=4z^2+1$ has no solution in the positive integers

Published on 10 Jul 2018 - 11:53

score 51 · Answer 2 · 2026-03-24 19:01:21

51

Views

Greatest common divisor of coefficients

Published on 24 Mar 2026 - 19:01

score 172 · Answer 3 · 2026-03-25 07:48:01

172

Views

Polynomial interpolation over the integers such that all coefficients are from the integers

Published on 25 Mar 2026 - 7:48

score 165 · Answer 4 · 2018-07-13 16:03:10

165

Views

Largest Nontrivial Integer Definition

Published on 13 Jul 2018 - 16:03

score 397 · Answer 5 · 2018-07-16 18:28:01

397

Views

Proof that the algebraic integers form a subring of $\mathbb{C}$

Published on 16 Jul 2018 - 18:28

score 56 · Answer 6 · 2026-03-25 20:59:56

56

Views

simplification of (i^j)%k

Published on 25 Mar 2026 - 20:59

score 860 · Answer 7 · 2026-03-25 09:29:50

860

Views

Find all real number(s) $x$ satisfying the equation $\{(x +1)^3\}$ = $x^3$ , where $\{y\}$ denotes the fractional part of $y$

Published on 25 Mar 2026 - 9:29

score 154 · Answer 8 · 2026-03-25 14:39:20

154

Views

How to derive the formula to compute an integer window number for given window width and overlap fraction (example given)

Published on 25 Mar 2026 - 14:39

score 260 · Answer 9 · 2018-07-19 09:37:14

260

Views

Problem with reading a proof: uniqueness of integer solution to $0<(za-1)a^{q-1}<1$

Published on 19 Jul 2018 - 9:37

score 72 · Answer 10 · 2026-03-25 19:04:14

72

Views

can anyone give me a function on the integer defined as $f_{n}(f_{n}(x))=x$ please?

Published on 25 Mar 2026 - 19:04

score 69 · Answer 11 · 2018-07-20 04:05:59

69

Views

Solving $a^3+a^2|a+x|+|a^2x+1|=1$

Published on 20 Jul 2018 - 4:05

score 213 · Answer 12 · 2018-07-24 08:07:07

213

Views

Solve $a^4 + b^4 + c^4 +l^4 = a^2b^2+a^2c^2+a^2l^2+b^2c^2+b^2l^2+c^2l^2$ in integers

Published on 24 Jul 2018 - 8:07

score 791 · Answer 13 · 2026-03-25 04:39:26

791

Views

Prove that the ordering relation $<_Z$ on the integers is well defined.

Published on 25 Mar 2026 - 4:39

score 162 · Answer 14 · 2018-07-25 15:16:23

162

Views

Recurrence relation of $1, 3, 3, 15, 5, 35, 7, 63, 9, 99, 11, 143, 13$

Published on 25 Jul 2018 - 15:16

score 91 · Answer 15 · 2026-03-25 13:55:08

91

Views

How many compositions does 40 have (with up to 5 addends), with each positive integer addend between 2 and 12?

Published on 25 Mar 2026 - 13:55

List Question

Prove the equation $\left(2x^2+1\right)\left(2y^2+1\right)=4z^2+1$ has no solution in the positive integers

Greatest common divisor of coefficients

Polynomial interpolation over the integers such that all coefficients are from the integers

Largest Nontrivial Integer Definition

Proof that the algebraic integers form a subring of $\mathbb{C}$

simplification of (i^j)%k

Find all real number(s) $x$ satisfying the equation $\{(x +1)^3\}$ = $x^3$ , where $\{y\}$ denotes the fractional part of $y$

How to derive the formula to compute an integer window number for given window width and overlap fraction (example given)

Problem with reading a proof: uniqueness of integer solution to $0<(za-1)a^{q-1}<1$

can anyone give me a function on the integer defined as $f_{n}(f_{n}(x))=x$ please?

Solving $a^3+a^2|a+x|+|a^2x+1|=1$

Solve $a^4 + b^4 + c^4 +l^4 = a^2b^2+a^2c^2+a^2l^2+b^2c^2+b^2l^2+c^2l^2$ in integers

Prove that the ordering relation $<_Z$ on the integers is well defined.

Recurrence relation of $1, 3, 3, 15, 5, 35, 7, 63, 9, 99, 11, 143, 13$

How many compositions does 40 have (with up to 5 addends), with each positive integer addend between 2 and 12?

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