Question

Prove that for $\forall m \ge 2$, $\dfrac{1}{2}(a^4 + b^4 + c^4) \mid [(ab)^{2^m} + (bc)^{2^m} + (ca)^{2^m}]$.

score 176 · Answer 1 · 2026-04-15 08:37:55

176

Views

Prove that for $\forall m \ge 2$, $\dfrac{1}{2}(a^4 + b^4 + c^4) \mid [(ab)^{2^m} + (bc)^{2^m} + (ca)^{2^m}]$.

Published on 15 Apr 2026 - 8:37

score 44 · Answer 2 · 2026-04-08 17:38:43

44

Views

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score 112 · Answer 3 · 2026-04-11 19:15:08

112

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score 160 · Answer 4 · 2026-04-14 21:26:52

160

Views

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score 153 · Answer 5 · 2026-04-10 20:37:39

153

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997

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140

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126

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217

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159

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score 230 · Answer 11 · 2026-04-15 10:24:01

230

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score 101 · Answer 12 · 2026-04-16 08:41:34

101

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351

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342

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score 114 · Answer 15 · 2026-04-14 23:46:05

114

Views

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List Question

Prove that for $\forall m \ge 2$, $\dfrac{1}{2}(a^4 + b^4 + c^4) \mid [(ab)^{2^m} + (bc)^{2^m} + (ca)^{2^m}]$.

Small problem in attempt to find $3$ Pythagorean triples to make a right angle.

Providing divisibility condition given fraction identity

Of a given perimeter, do there exist infinitely many right-angled triangles?

Can I narrow my search range in seeking solutions for equations?

Pythagorean triple with hypotenuse a power of $2$

An interesting question about greatest common divisor (gcd) of three positive integers which form a primitive Pythagorean triple

A sequence of right triangles

Proof Writing For Pythagorean Triple “Reduction” Problem

Pre-calculus method for finding the 'neat' value $\sin(\frac{\pi}{3})=\frac{\sqrt3}{2}$?

Prove that the area of the trangles are equal.

Prove that $Q$ is rational if and only if $t$ is rational

Looking for references to Pythagorean triple subsets

A pattern within the differences of pythagorean triples?

Pythagoras 3-4-5 tetrahedron triple, geometric puzzle

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