Question

Prove that there do not exist integers that satisfy the system

score 300 · Answer 1 · 2017-01-05 21:24:44

300

Views

Prove that there do not exist integers that satisfy the system

Published on 05 Jan 2017 - 21:24

score 464 · Answer 2 · 2017-01-06 10:39:09

464

Views

Pell equation ($x^2 - ny^2 = 1$): Why does $(x_{1}+y_{1}{\sqrt {n}})^{k}$ give all solutions?

Published on 06 Jan 2017 - 10:39

score 173 · Answer 3 · 2017-01-06 17:14:48

173

Views

Find all prime numbers p,q

Published on 06 Jan 2017 - 17:14

score 259 · Answer 4 · 2017-01-06 20:14:00

259

Views

Find all positive integer solutions to the equation $\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{c^2}$

Published on 06 Jan 2017 - 20:14

score 83 · Answer 5 · 2017-01-06 22:07:27

83

Views

Find all of positive integers $k, m, n$ such that $T := \frac{2kmn(m^2 - n^2)}{m^2 +n^2} \in \mathbb{Z} .$

Published on 06 Jan 2017 - 22:07

score 264 · Answer 6 · 2017-01-07 08:38:08

264

Views

Integer solutions for $a+b+c+d=0$, $a^3+b^3+c^3+d^3=24$

Published on 07 Jan 2017 - 8:38

score 76 · Answer 7 · 2017-01-07 20:05:56

76

Views

Find all odd integers $u,v,r,s$ such that $u^2-v^2=3r^2+s^2$

Published on 07 Jan 2017 - 20:05

score 164 · Answer 8 · 2026-03-30 16:07:46

164

Views

Find the $\gcd[x+y+z; x^2+xy+z^2; y^2+yz+z^2; z^2+zx+x^2]$

Published on 30 Mar 2026 - 16:07

score 417 · Answer 9 · 2017-01-08 13:46:02

417

Views

Find integers solutions of $x^2+7=y^5$

Published on 08 Jan 2017 - 13:46

score 997 · Answer 10 · 2017-01-08 15:26:24

997

Views

Show that $y^2=x^3+23$ has no integer solutions (hint: use $y^2+4$)

Published on 08 Jan 2017 - 15:26

score 2.3k · Answer 11 · 2026-04-04 02:47:18

2.3k

Views

Fermat's last theorem over finite fields

Published on 04 Apr 2026 - 2:47

score 479 · Answer 12 · 2017-01-08 17:06:04

479

Views

Exponential diophantine equation involving a prime number

Published on 08 Jan 2017 - 17:06

score 141 · Answer 13 · 2017-01-08 22:57:04

141

Views

Find all integer numbers $k$,$l$,$m$,$n$ for which $3^k$ • $5^l$ + $7^m$ = $2^n$

Published on 08 Jan 2017 - 22:57

score 736 · Answer 14 · 2017-01-10 16:54:18

736

Views

$x^4+ry^4=z^4$: find primitive Diophantine solutions with prime $r$.

Published on 10 Jan 2017 - 16:54

score 104 · Answer 15 · 2026-03-25 19:02:22

104

Views

What values can $2^j-3^k$ have?

Published on 25 Mar 2026 - 19:02

List Question

Prove that there do not exist integers that satisfy the system

Pell equation ($x^2 - ny^2 = 1$): Why does $(x_{1}+y_{1}{\sqrt {n}})^{k}$ give all solutions?

Find all prime numbers p,q

Find all positive integer solutions to the equation $\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{c^2}$

Find all of positive integers $k, m, n$ such that $T := \frac{2kmn(m^2 - n^2)}{m^2 +n^2} \in \mathbb{Z} .$

Integer solutions for $a+b+c+d=0$, $a^3+b^3+c^3+d^3=24$

Find all odd integers $u,v,r,s$ such that $u^2-v^2=3r^2+s^2$

Find the $\gcd[x+y+z; x^2+xy+z^2; y^2+yz+z^2; z^2+zx+x^2]$

Find integers solutions of $x^2+7=y^5$

Show that $y^2=x^3+23$ has no integer solutions (hint: use $y^2+4$)

Fermat's last theorem over finite fields

Exponential diophantine equation involving a prime number

Find all integer numbers $k$,$l$,$m$,$n$ for which $3^k$ • $5^l$ + $7^m$ = $2^n$

$x^4+ry^4=z^4$: find primitive Diophantine solutions with prime $r$.

What values can $2^j-3^k$ have?

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