List questions from infinite-descent

Published on 04 May 2026 - 19:39

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Proof By Descent FLT

Published on 29 Apr 2026 - 12:24

105

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Proving $x^2-y^2 = 2xyz$ has no integer solutions greater than 0.

Published on 03 May 2026 - 14:41

879

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Show $x^2$ + $y^2$ + $z^2$ = $2xyz$ has no non-trivial solutions using infinite descent.

Published on 29 Apr 2026 - 12:50

902

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Find all $x$ such that $4^{27}+4^{1000}+4^{x}$ is a perfect square.

Published on 04 May 2026 - 13:48

357

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Geometric proof of number theory result: If the geometric and quadratic means of integers $a$ and $b$ are themselves integers, then $a=b$

Published on 07 May 2026 - 10:12

1.1k

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Show that $x^2 + y^2 = 3$ has no rational points

Published on 07 May 2026 - 16:51

461

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How to solve $x^2+y^2=pz^2$ in $x,y,z\in\mathbb{N}$ if $p$ is such a prime that $p\equiv 3 \pmod 4$?

Published on 03 May 2026 - 9:22

6.4k

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What is an example of a proof by minimal counterexample?

Published on 29 Apr 2026 - 12:50

401

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Solving the homogeneous Diophantine equation $x^3 + 2y^3 = 7z^3$ for $x,y,z \in \mathbb{Q}$

Published on 07 May 2026 - 18:59

1.1k

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Lamé's proof of Fermat Last Theorem for n=3

Published on 29 Apr 2026 - 12:49

949

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Combinatorics problems that can be solved via infinite descent

Published on 23 Apr 2026 - 3:36

87

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Given integer $b \gt 1$ use infinite descent to prove that every integer $m \gt 0$ has one and only one Base-$b$ representation.

Published on 23 Apr 2026 - 10:17

48

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Structured Theorems(Programs) in Number Theory Proving Logical Conjunctions Using Infinite Descent

Published on 23 Apr 2026 - 19:40

60

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How to prove that the difference of squares of two natural numbers can't be a perfect square if their sum is a perfect square?

Published on 22 Apr 2026 - 11:27

List Question

Proof of irrationality

Proof By Descent FLT

Proving $x^2-y^2 = 2xyz$ has no integer solutions greater than 0.

Show $x^2$ + $y^2$ + $z^2$ = $2xyz$ has no non-trivial solutions using infinite descent.

Find all $x$ such that $4^{27}+4^{1000}+4^{x}$ is a perfect square.

Geometric proof of number theory result: If the geometric and quadratic means of integers $a$ and $b$ are themselves integers, then $a=b$

Show that $x^2 + y^2 = 3$ has no rational points

How to solve $x^2+y^2=pz^2$ in $x,y,z\in\mathbb{N}$ if $p$ is such a prime that $p\equiv 3 \pmod 4$?

What is an example of a proof by minimal counterexample?

Solving the homogeneous Diophantine equation $x^3 + 2y^3 = 7z^3$ for $x,y,z \in \mathbb{Q}$

Lamé's proof of Fermat Last Theorem for n=3

Combinatorics problems that can be solved via infinite descent

Given integer $b \gt 1$ use infinite descent to prove that every integer $m \gt 0$ has one and only one Base-$b$ representation.

Structured Theorems(Programs) in Number Theory Proving Logical Conjunctions Using Infinite Descent

How to prove that the difference of squares of two natural numbers can't be a perfect square if their sum is a perfect square?

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