2
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$Given$:

$ASC$ 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:

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

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closed as off-topic by greenturtle3141, Glorfindel, Peregrine Rook, w l, Omega Krypton Jul 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.

  • 1
    $\begingroup$ 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. $\endgroup$ – greenturtle3141 Jul 7 at 16:53
  • $\begingroup$ (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.) $\endgroup$ – Rubio Jul 7 at 22:22
3
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As A, S, C are single digit numbers, $A=2,S=4,C=8$.
So we have $$2^4 2^{248} + 4^8 4^{248} + 8^2 8^{248} =4^{126} + 4^{256} + 4^{375} \equiv 6+6+4 \equiv 6$$.

Reason

Odd power of $4 \equiv 4$ (last digit) and
Even power of $4\equiv6$ (last digit)

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