Let $ a_1, a_2, ..., a_ {1994} $ be integers such that $ a_1 + a_2 + ... + a_{1994} = 1994 ^{1994} $ . Determine the remainder of the division of $ a ^ 3_1 + a ^ 3_2 + ... + a ^ 3_{1994} $ with $6$.
Source: North Macedonian Mathematical Olympiad 1996 p4
Tags: Sum, number theory, remainder
Let $ a_1, a_2, ..., a_ {1994} $ be integers such that $ a_1 + a_2 + ... + a_{1994} = 1994 ^{1994} $ . Determine the remainder of the division of $ a ^ 3_1 + a ^ 3_2 + ... + a ^ 3_{1994} $ with $6$.