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Euler on trial (Posted on 2015-05-14)

Euler proposed that the equation a⁴+b⁴+c⁴ =d⁴ had no solutions in integers (excluding the trivial 0,0,0 of course).

Nowadays, is it true or not?

No Solution Yet Submitted by Ady TZIDON

Rating: 1.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: Using the Internet (spoiler)

| Comment 3 of 4 |

(In reply to Using the Internet (spoiler) by Steve Herman)

Per that same paper, the smallest solution is:

95800^4 + 217519^4 + 414560^4 = 422481^4

This is the only solution where all terms are co-prime and under a billion.

The only other solution under a billion is achieved by doubling each of the terms.

Edited on May 14, 2015, 7:10 pm

Posted by Steve Herman on 2015-05-14 13:03:36

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