Question

the system of diophantine equations: $x+y=a^3$; $xy=\dfrac{a^6-b^3}{3}$ has only trivial solutions.

score 189 · Answer 1 · 2016-03-14 20:37:51

189

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the system of diophantine equations: $x+y=a^3$; $xy=\dfrac{a^6-b^3}{3}$ has only trivial solutions.

Published on 14 Mar 2016 - 20:37

score 102 · Answer 2 · 2026-04-11 18:59:32

102

Views

is A an even number?

Published on 11 Apr 2026 - 18:59

score 144 · Answer 3 · 2026-04-04 05:41:47

144

Views

Find all natural solutions of $14x+21y=91$

Published on 04 Apr 2026 - 5:41

score 68 · Answer 4 · 2026-04-01 13:30:49

68

Views

Representations of some primes as $3x^2-4y^2$?

Published on 01 Apr 2026 - 13:30

score 187 · Answer 5 · 2026-04-12 06:33:34

187

Views

Parametric solution of the Diophantine equation $\frac{3}{n}=\sum\frac{1}{a}$

Published on 12 Apr 2026 - 6:33

score 87 · Answer 6 · 2026-04-09 05:27:37

87

Views

Diophantine Factorial Equation

Published on 09 Apr 2026 - 5:27

score 255 · Answer 7 · 2026-04-06 14:21:34

255

Views

Seeking general methods to attack $ax^4+bx^3y+cx^2y^2+dxy^3+ey^4=z^2$ in integers/rationals

Published on 06 Apr 2026 - 14:21

score 1k · Answer 8 · 2026-03-25 23:38:18

1k

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Is there any algorithm to find all the solutions of the following special linear Diophantine system?

Published on 25 Mar 2026 - 23:38

score 56 · Answer 9 · 2026-04-10 17:22:14

56

Views

How many solutions in integers to the following equation

Published on 10 Apr 2026 - 17:22

score 200 · Answer 10 · 2016-03-21 18:44:18

200

Views

Let $x,y,z$ be 3 coprime integers where $u|x, v|y, w|z$, is $x^3+y^3+z^3\equiv 0 \pmod{(uvw)^3}?$

Published on 21 Mar 2016 - 18:44

score 194 · Answer 11 · 2026-03-29 11:13:37

194

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Trying to prove $c^3a^2+(9c^2-b^2)a+(27c-10b)=0$ has no positive integer solutions

Published on 29 Mar 2026 - 11:13

score 153 · Answer 12 · 2026-04-11 20:14:22

153

Views

Prime solutions to an exponential diophantine equation

Published on 11 Apr 2026 - 20:14

score 56 · Answer 13 · 2016-03-24 01:22:25

56

Views

Number of integer solutions $(x, y)$ of $x(x+6) = y^2 + k$ for different integer values of $k$

Published on 24 Mar 2016 - 1:22

score 73 · Answer 14 · 2016-03-24 03:26:45

73

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Integer solutions of $\sum_{j=1}^m\frac{n-m}{j}+\sum_{j=m+1}^n\frac{n}{j}=k$

Published on 24 Mar 2016 - 3:26

score 482 · Answer 15 · 2016-03-25 16:33:34

482

Views

Find the largest integer $n$ such that $n^2$ is the difference of two consecutive cubes and $2n +79$ is a perfect square.

Published on 25 Mar 2016 - 16:33

List Question

the system of diophantine equations: $x+y=a^3$; $xy=\dfrac{a^6-b^3}{3}$ has only trivial solutions.

is A an even number?

Find all natural solutions of $14x+21y=91$

Representations of some primes as $3x^2-4y^2$?

Parametric solution of the Diophantine equation $\frac{3}{n}=\sum\frac{1}{a}$

Diophantine Factorial Equation

Seeking general methods to attack $ax^4+bx^3y+cx^2y^2+dxy^3+ey^4=z^2$ in integers/rationals

Is there any algorithm to find all the solutions of the following special linear Diophantine system?

How many solutions in integers to the following equation

Let $x,y,z$ be 3 coprime integers where $u|x, v|y, w|z$, is $x^3+y^3+z^3\equiv 0 \pmod{(uvw)^3}?$

Trying to prove $c^3a^2+(9c^2-b^2)a+(27c-10b)=0$ has no positive integer solutions

Prime solutions to an exponential diophantine equation

Number of integer solutions $(x, y)$ of $x(x+6) = y^2 + k$ for different integer values of $k$

Integer solutions of $\sum_{j=1}^m\frac{n-m}{j}+\sum_{j=m+1}^n\frac{n}{j}=k$

Find the largest integer $n$ such that $n^2$ is the difference of two consecutive cubes and $2n +79$ is a perfect square.

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