Question

What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$

score 501 · Answer 1 · 2026-03-22 10:42:37

501

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What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$

Published on 22 Mar 2026 - 10:42

score 223 · Answer 2 · 2020-04-06 22:00:23

223

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Infinite descent argument in the case of $x^5+y^5=z^5$.

Published on 06 Apr 2020 - 22:00

score 239 · Answer 3 · 2026-03-25 16:08:05

239

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Proving Diophantine Equation has no solution using Legendre Symbol

Published on 25 Mar 2026 - 16:08

score 746 · Answer 4 · 2020-04-09 18:43:33

746

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If two positive integers m and n, both bigger than 1, satisfy the equation 2005^2 + m^2 = 2004^2 + n^2 , find the value of m + n – 200

Published on 09 Apr 2020 - 18:43

score 679 · Answer 5 · 2020-04-10 10:08:51

679

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Let $x,y\in\Bbb R$ such that $x ^2 + y^2 = 2x – 2y + 2$. What is the largest possible value of $x^2 + y^2 -\sqrt{32}$??

Published on 10 Apr 2020 - 10:08

score 73 · Answer 6 · 2020-04-10 12:59:10

73

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A system of quadratic Diophantine equations with six variables

Published on 10 Apr 2020 - 12:59

score 69 · Answer 7 · 2026-04-01 01:11:45

69

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“Factoring” Diophantine approximations

Published on 01 Apr 2026 - 1:11

score 188 · Answer 8 · 2026-03-27 23:23:19

188

Views

Quickly Finding Positive Solutions to Diophantine Equations

Published on 27 Mar 2026 - 23:23

score 56 · Answer 9 · 2026-03-29 00:00:10

56

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Find solutions of $f(2020)x+f(2019)y=1$ where $f$ is Fibonacci sequence

Published on 29 Mar 2026 - 0:00

score 57 · Answer 10 · 2020-04-12 04:43:08

57

Views

$x^2 + 4xy = 10^{100}$ how many solutions

Published on 12 Apr 2020 - 4:43

score 112 · Answer 11 · 2026-03-26 20:40:43

112

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Show that $x^3+3y^3+9z^3-9xyz=1$ has infinitely many integer solutions.

Published on 26 Mar 2026 - 20:40

score 68 · Answer 12 · 2026-03-25 23:36:42

68

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How to avoid nested loops intelligently with the computer when solving Diophantine equations with finite range of variables?

Published on 25 Mar 2026 - 23:36

score 155 · Answer 13 · 2026-03-27 13:03:28

155

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How many ways can $2^{2012}$ be expressed as the sum of four (not necessarily distinct) positive squares?

Published on 27 Mar 2026 - 13:03

score 266 · Answer 14 · 2020-04-14 10:25:53

266

Views

What are the integer solutions to $5x^3=y^2+1$?

Published on 14 Apr 2020 - 10:25

score 96 · Answer 15 · 2020-04-15 01:02:56

96

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What is the importance of the Diophantine inequality $\frac{1}{p} + \frac{1}{q} + \frac{1}{r} > 1$?

Published on 15 Apr 2020 - 1:02

List Question

What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$

Infinite descent argument in the case of $x^5+y^5=z^5$.

Proving Diophantine Equation has no solution using Legendre Symbol

If two positive integers m and n, both bigger than 1, satisfy the equation 2005^2 + m^2 = 2004^2 + n^2 , find the value of m + n – 200

Let $x,y\in\Bbb R$ such that $x ^2 + y^2 = 2x – 2y + 2$. What is the largest possible value of $x^2 + y^2 -\sqrt{32}$??

A system of quadratic Diophantine equations with six variables

“Factoring” Diophantine approximations

Quickly Finding Positive Solutions to Diophantine Equations

Find solutions of $f(2020)x+f(2019)y=1$ where $f$ is Fibonacci sequence

$x^2 + 4xy = 10^{100}$ how many solutions

Show that $x^3+3y^3+9z^3-9xyz=1$ has infinitely many integer solutions.

How to avoid nested loops intelligently with the computer when solving Diophantine equations with finite range of variables?

How many ways can $2^{2012}$ be expressed as the sum of four (not necessarily distinct) positive squares?

What are the integer solutions to $5x^3=y^2+1$?

What is the importance of the Diophantine inequality $\frac{1}{p} + \frac{1}{q} + \frac{1}{r} > 1$?

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