Question

Find the positive integer solutions for the equation $x^y-y^x=1$

score 119 · Answer 1 · 2016-09-14 11:44:59

119

Views

Find the positive integer solutions for the equation $x^y-y^x=1$

Published on 14 Sep 2016 - 11:44

score 60 · Answer 2 · 2016-09-14 13:05:21

60

Views

Further question on Diophantine equations of form $ax+by=c$

Published on 14 Sep 2016 - 13:05

score 251 · Answer 3 · 2016-09-14 17:21:33

251

Views

Mordell type diophantine equation

Published on 14 Sep 2016 - 17:21

score 2.1k · Answer 4 · 2016-09-14 20:30:22

2.1k

Views

How many ordered pairs of integers satisfy the equation $\frac{7}{x}+\frac{3}{y}=\frac{1}{4}$?

Published on 14 Sep 2016 - 20:30

score 113 · Answer 5 · 2016-09-16 17:35:10

113

Views

Diophantine parametrization, can replace $5$ by some other number?

Published on 16 Sep 2016 - 17:35

score 269 · Answer 6 · 2016-09-16 19:16:53

269

Views

How do I prove this theorem about coprime numbers?

Published on 16 Sep 2016 - 19:16

score 453 · Answer 7 · 2026-03-25 22:06:32

453

Views

Is the solution of the equation $ 2\arctan(x) = x $ a rational multiple of $\pi$?

Published on 25 Mar 2026 - 22:06

score 156 · Answer 8 · 2016-09-17 12:53:24

156

Views

Integer solutions to $10^k + 332 = 3n^2$.

Published on 17 Sep 2016 - 12:53

score 147 · Answer 9 · 2016-09-18 11:14:45

147

Views

Exactly 6 integer solutions

Published on 18 Sep 2016 - 11:14

score 2.1k · Answer 10 · 2026-03-31 06:33:36

2.1k

Views

For some natural number $N$,the number of positive integral $'x'$ satisfying the equation is?

Published on 31 Mar 2026 - 6:33

score 94 · Answer 11 · 2016-09-19 11:35:47

94

Views

Three Diophantine equations in three variables, finding $x+y+z$

Published on 19 Sep 2016 - 11:35

score 648 · Answer 12 · 2016-09-19 18:34:41

648

Views

The sum of the cubes of two different prime numbers is 5256.

Published on 19 Sep 2016 - 18:34

score 269 · Answer 13 · 2026-03-27 07:18:38

269

Views

Does the 3.3.3 equation $x_1^3+x_2^3+x_3^3=y_1^3+y_2^3+y_3^3$ have a complete integer or rational solution?

Published on 27 Mar 2026 - 7:18

score 684 · Answer 14 · 2026-04-02 23:41:25

684

Views

How many natural solutions to $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 24$ if $x_1 + x_2 + x_3 > x_4 + x_5 + x_6$?

Published on 02 Apr 2026 - 23:41

score 180 · Answer 15 · 2016-09-21 05:34:19

180

Views

On fifth powers $x_1^5+x_2^5+\dots = y_1^5+y_2^5+\dots$

Published on 21 Sep 2016 - 5:34

List Question

Find the positive integer solutions for the equation $x^y-y^x=1$

Further question on Diophantine equations of form $ax+by=c$

Mordell type diophantine equation

How many ordered pairs of integers satisfy the equation $\frac{7}{x}+\frac{3}{y}=\frac{1}{4}$?

Diophantine parametrization, can replace $5$ by some other number?

How do I prove this theorem about coprime numbers?

Is the solution of the equation $ 2\arctan(x) = x $ a rational multiple of $\pi$?

Integer solutions to $10^k + 332 = 3n^2$.

Exactly 6 integer solutions

For some natural number $N$,the number of positive integral $'x'$ satisfying the equation is?

Three Diophantine equations in three variables, finding $x+y+z$

The sum of the cubes of two different prime numbers is 5256.

Does the 3.3.3 equation $x_1^3+x_2^3+x_3^3=y_1^3+y_2^3+y_3^3$ have a complete integer or rational solution?

How many natural solutions to $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 24$ if $x_1 + x_2 + x_3 > x_4 + x_5 + x_6$?

On fifth powers $x_1^5+x_2^5+\dots = y_1^5+y_2^5+\dots$

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