1989 AIME Problem 9

One of Euler's conjectures was disproved in the 1960s by three American mathematicians when they showed there was a positive integer n such that 133^5+110^5+84^5+27^5=n^{5}_{}. Find the value of n^{}_{}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.