Question

Solving a particular system of Diophantine equations

score 173 · Answer 1 · 2026-04-11 05:31:22

173

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Solving a particular system of Diophantine equations

Published on 11 Apr 2026 - 5:31

score 162 · Answer 2 · 2026-04-06 19:26:21

162

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Is there a way to find the values of 3 variables with just one equation?

Published on 06 Apr 2026 - 19:26

score 145 · Answer 3 · 2026-04-16 04:46:23

For $5b^2+4=n^2$, prove that $b=\frac{1}{5}(\lambda_2-\lambda_1)(\lambda_2^k-\lambda_1^k)$ where $\lambda_1, \lambda_2$ are roots of $x^2-3x+1=0$.

score 52 · Answer 4 · 2026-04-14 02:55:50

52

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Show that the Diophantine equation only have trivial solution

Published on 14 Apr 2026 - 2:55

score 77 · Answer 5 · 2026-04-12 19:13:03

77

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Estimating number of lattice points on a hyperbola

Published on 12 Apr 2026 - 19:13

score 40 · Answer 6 · 2026-04-16 02:31:06

40

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Find all solutions of $\frac{2}{x}+\frac{8}{y}=\frac13$

Published on 16 Apr 2026 - 2:31

score 144 · Answer 7 · 2026-04-14 20:57:11

144

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On solutions to special eighth/fourth powers $a^8+b^4 = c^8+d^4$?

Published on 14 Apr 2026 - 20:57

score 96 · Answer 8 · 2026-04-17 13:36:27

96

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On the Diophantine equation $2(x^3 - x) = y^3 - y$

Published on 17 Apr 2026 - 13:36

score 112 · Answer 9 · 2026-04-14 02:12:46

112

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Sum of two odd cubes plus four times a cube is zero

Published on 14 Apr 2026 - 2:12

score 97 · Answer 10 · 2026-04-11 23:55:27

97

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Diophantine equation $a^{2} = b^{4} + b^{3} + b^{2} + b + 1$

Published on 11 Apr 2026 - 23:55

score 305 · Answer 11 · 2026-04-14 11:04:21

305

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Pythagorean quintuple $x^2+y^2+z^2+w^2=u^2$ has infinite solutions. Is it difficult to find the general formula of its integer solution?

Published on 14 Apr 2026 - 11:04

score 43 · Answer 12 · 2026-04-15 23:02:47

43

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Markov Chains and Diophantine Equations

Published on 15 Apr 2026 - 23:02

score 65 · Answer 13 · 2026-04-14 11:24:34

65

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Solutions to an elliptic curve equation involving a prime

Published on 14 Apr 2026 - 11:24

score 277 · Answer 14 · 2026-04-11 02:11:27

277

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How could one prove that there are no positive integers for which a given expression is a perfect square?

Published on 11 Apr 2026 - 2:11

score 302 · Answer 15 · 2026-04-13 13:59:44

302

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Diophantine equation ${x ^ 2}+{y ^ 2}+{z ^ 2}={m ^ 2}+{n ^ 2} $ has infinite solutions. What is its general solution formula?

Published on 13 Apr 2026 - 13:59

List Question

Solving a particular system of Diophantine equations

Is there a way to find the values of 3 variables with just one equation?

For $5b^2+4=n^2$, prove that $b=\frac{1}{5}(\lambda_2-\lambda_1)(\lambda_2^k-\lambda_1^k)$ where $\lambda_1, \lambda_2$ are roots of $x^2-3x+1=0$.

Show that the Diophantine equation only have trivial solution

Estimating number of lattice points on a hyperbola

Find all solutions of $\frac{2}{x}+\frac{8}{y}=\frac13$

On solutions to special eighth/fourth powers $a^8+b^4 = c^8+d^4$?

On the Diophantine equation $2(x^3 - x) = y^3 - y$

Sum of two odd cubes plus four times a cube is zero

Diophantine equation $a^{2} = b^{4} + b^{3} + b^{2} + b + 1$

Pythagorean quintuple $x^2+y^2+z^2+w^2=u^2$ has infinite solutions. Is it difficult to find the general formula of its integer solution?

Markov Chains and Diophantine Equations

Solutions to an elliptic curve equation involving a prime

How could one prove that there are no positive integers for which a given expression is a perfect square?

Diophantine equation ${x ^ 2}+{y ^ 2}+{z ^ 2}={m ^ 2}+{n ^ 2} $ has infinite solutions. What is its general solution formula?

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