Uninterestingly Interesting

Algebra Level 2

True or False (or Ambiguous )

178 2 12 + 184 1 12 12 = 192 2 12 12 \sqrt[12]{1782^{12} + 1841^{12}} = \sqrt[12]{1922^{12}}

True False Ambiguous

Mohammad Farhat by Mohammad Farhat , 16, Singapore

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3 solutions

Chew-Seong Cheong
Oct 17, 2018

Note that the LHS 178 2 12 + 184 1 12 1782^{12} + 1841^{12} is odd, while the RHS 192 2 12 1922^{12} is even. Therefore the equation is false .

11 Helpful 0 Interesting 0 Brilliant 0 Confused
Jordan Cahn
Oct 17, 2018

To pull out the biggest possible hammer: By Fermat's Last Theorem this must be false .

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Yeah! That was the main objective: Identify Fermat's Last Theorem

Mohammad Farhat - 2 years, 7 months ago
Mohammad Farhat
Oct 18, 2018

Relevant wiki: Fermat's Last Theorem

Fermat's Last Theorem says that there are no solutions to the equation x n + y n = z n x^n + y^n = z^n where n ≥ 3 n \geq 3 and this problem is clearly a violation of it.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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