List questions from infinite-descent

Published on 06 Sep 2019 - 0:50

686

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

Published on 05 Aug 2014 - 16:09

1k

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

Published on 14 Nov 2014 - 11:52

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

157

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

Published on 17 Aug 2016 - 1:13

992

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

Published on 04 Jan 2017 - 15:26

2.3k

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

Published on 04 Mar 2017 - 7:07

129

Views

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

Published on 14 Mar 2026 - 7:32

240

Views

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

Published on 10 Nov 2023 - 11:11

94

Views

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

Published on 04 Mar 2024 - 11:20

150

Views

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

Published on 02 Apr 2015 - 14:11

539

Views

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

Published on 09 Jun 2015 - 19:49

1.1k

Views

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

Published on 12 Nov 2015 - 1:38

212

Views

Fermat's Challenge of composition of numbers

Published on 22 Mar 2026 - 8:30

422

Views

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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