Wednesday, September 26th

Problem

Find the minimum n for which 1999 can be written as the sum of n forth powers of positive integers.

Solution

Notice that

$1999=3\cdot5^4+3^4+2\cdot 2^4+11\cdot 1^4$ 

which gives the value of $n=17$. Brute force over the few cases shows that this is the minimum