# What is the Last Digit in the Result of the given Expression? [closed]

$$Given$$:

$$ASC$$ is a concatenated number with distinct digits.

$$S$$ is square of $$A$$, $$C$$ is cube of $$A$$

Deduce the last digit of the following Expression through Deductive Reasoning only:

\begin{align}A^S&\times A^{ASC}\\ +\space S^C&\times S^{ASC}\\ +\,C^A&\times C^{ASC}\end{align}

## closed as off-topic by greenturtle3141, Glorfindel, Peregrine Rook, w l, Omega KryptonJul 8 at 11:36

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – greenturtle3141, Glorfindel, w l, Omega Krypton
If this question can be reworded to fit the rules in the help center, please edit the question.

• I'm VTC because determining A, S, C is completely trivial, and this reduces to a very routine number theory problem, so this is not a puzzle. – greenturtle3141 Jul 7 at 16:53
• (I'm also inclined to close as not-a-puzzle on different grounds: that this is something to recognize more than something to actually solve.) – Rubio Jul 7 at 22:22

As A, S, C are single digit numbers, $$A=2,S=4,C=8$$.
So we have $$2^4 2^{248} + 4^8 4^{248} + 8^2 8^{248} =4^{126} + 4^{256} + 4^{375} \equiv 6+6+4 \equiv 6$$.
Odd power of $$4 \equiv 4$$ (last digit) and
Even power of $$4\equiv6$$ (last digit)