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Soviet Union 11

Source: IMO LongList 1959-1966 Problem 54

September 2, 2004
number theorydecimal representationDigitsLast digitmodular arithmeticIMO ShortlistIMO Longlist

Problem Statement

We take 100100 consecutive natural numbers a1,a_{1}, a2,a_{2}, ...,..., a100.a_{100}. Determine the last two digits of the number a18+a28+...+a1008.a_{1}^{8}+a_{2}^{8}+...+a_{100}^{8}.
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