List questions from infinite-descent

Published on 25 Mar 2026 - 6:09

689

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If $\gcd(a,b)=1$, then every odd factor of $a^2 + 3b^2$ has this same form

Published on 12 Apr 2026 - 8:33

1k

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Why is this proof that $\sqrt{2}$ is irrational titled as "Proof by infinite descent"?

Published on 13 Apr 2026 - 22:02

224

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

Published on 01 Apr 2026 - 20:52

159

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Proofs by infinite descent on the number of prime factors of an integer

Published on 15 Apr 2026 - 2:31

995

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Show that $x^3+2y^3+4z^3=0 $ has no non trivial solutions without using infinite descent

Published on 14 Apr 2026 - 17:00

2.3k

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Proving that there does not exist an infinite descending sequence of naturals using minimal counterexample

Published on 17 Apr 2026 - 13:49

131

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Can the irrationality of $\sqrt3$ be proven geometrically by infinite descent, similarly to Tom Apostol's proof of the irrationality of $\sqrt2$?

Published on 11 Apr 2026 - 20:20

242

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Mordell's Theorem and Fermat's Last Theorem for $n=4$: A general method?

Published on 10 Apr 2026 - 3:39

95

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Solve $3a^2 + 3ab + b^2 - p^3 = 0$ using infinite descent or otherwise?

Published on 06 Apr 2026 - 18:14

153

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If $a,b,c$ are integers such that $4a^3+2b^3+c^3=6abc$, is $a=b=c=0$?

Published on 17 Apr 2026 - 7:16

540

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find all natural solution that satisfy $x^2+y^2 = 3z^2$

Published on 25 Mar 2026 - 6:10

1.1k

Views

Fermat's infinite descent for finding the squares that sum to a prime

Published on 28 Mar 2026 - 16:03

214

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Fermat's Challenge of composition of numbers

Published on 09 Apr 2026 - 7:13

422

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Find all solutions to the equation $x^2 + y^2 + xy = (xy)^2$

Published on 23 Mar 2016 - 12:12

List Question

Proof Writing For Pythagorean Triple “Reduction” Problem

If $\gcd(a,b)=1$, then every odd factor of $a^2 + 3b^2$ has this same form

Why is this proof that $\sqrt{2}$ is irrational titled as "Proof by infinite descent"?

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

Proofs by infinite descent on the number of prime factors of an integer

Show that $x^3+2y^3+4z^3=0 $ has no non trivial solutions without using infinite descent

Proving that there does not exist an infinite descending sequence of naturals using minimal counterexample

Can the irrationality of $\sqrt3$ be proven geometrically by infinite descent, similarly to Tom Apostol's proof of the irrationality of $\sqrt2$?

Mordell's Theorem and Fermat's Last Theorem for $n=4$: A general method?

Solve $3a^2 + 3ab + b^2 - p^3 = 0$ using infinite descent or otherwise?

If $a,b,c$ are integers such that $4a^3+2b^3+c^3=6abc$, is $a=b=c=0$?

find all natural solution that satisfy $x^2+y^2 = 3z^2$

Fermat's infinite descent for finding the squares that sum to a prime

Fermat's Challenge of composition of numbers

Find all solutions to the equation $x^2 + y^2 + xy = (xy)^2$

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