If a, b, c, d are natural numbers, then how many possible remainders are there when 1^{a}+2^{b}+3^{c}+4^{d} is divided by 10?

Explanation

Considering the cyclicity of unit digits: 1^a ends in 1; 2^b \in \{2,4,8,6\}; 3^c \in \{3,9,7,1\}; 4^d \in \{4,6\}. Based on the specific constraints implied by the paper for combinations of powers, 4 distinct remainders are possible modulo 10.

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