Exercise 2.1.9 (Unit digit of a fourth power)

Question

Prove that any fourth power must have one of $0,1,5,6$ for its units digit.

Richard Ganaye · Accepted Answer

\begin{proof} 
We complete the array of Problem 8, where $n \equiv a \pmod{10}$.
$$
\begin{array}{c|cccccccccc}
a			& 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\
\hline
a^2 \mod {10}   & 0 & 1 & 4 & 9 & 6 & 5 & 6 & 9 & 4 & 1\
a^4 \mod {10}   & 0 & 1 & 6 & 1 & 6 & 5 & 6 & 1 & 6 & 1
\end{array}
$$
Therefore $n^4$ must have one of $0,1,5,6$ for its units digit.
\end{proof}

Exercise 2.1.9 (Unit digit of a fourth power)

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Exercise 2.1.9 (Unit digit of a fourth power)

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