Relative of 1729 1729

Number Theory Level 2

What is the smallest number which can be represented as sum of 2 2 4 t h 4^{th} powers in 2 2 different ways?


The answer is 635318657.

Mr. India by Mr. India , 17, India

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1 solution

Mr. India
May 16, 2019

635318657 = 5 9 4 + 15 8 4 = 13 3 4 + 13 4 4 635318657=59^4 + 158^4=133^4 + 134^4

Anyone having proof or any interesting article?

0 Helpful 0 Interesting 0 Brilliant 0 Confused

A list of such numbers

Detailed Analysis

I believe the above example was first found by Euler.

Sathvik Acharya - 2 years ago

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Thank you. Is there a proper way to find them?

Yes you are right

Mr. India - 2 years ago

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I am pretty sure that an elementary proof has not yet been found.

Sathvik Acharya - 2 years ago

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