Find a solution to:
x₁^4 + x₂^4 + x₃^4 + ... + x_n^4 = 1999

where each x_y is a distinct integer.

(Or prove that it is impossible).

The numbers can be only from 1 to 6, for 7^4 is greater than 1999. The sum 1^4+2^4+3^4+4^4+5^4 is less than 1999, so 6 should be in the sum. 1999-6^4=703, and it's easy to see that there's no way of getting that sum picking among 1^4, 2^4, 3^4, 4^4, and 5^4, so the problem is impossible.

Posted by Oskar on 2004-09-12 10:48:50