Euler proposed that the equation
had no solutions in integers (excluding the trivial 0,0,0 of course).
Nowadays, is it true or not?
(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