Remainder of Exponential Sum

CAT 2004 Slot 1 · Quantitative Ability · Easy · Number System

This is an easy Quantitative Ability question from the CAT 2004 Slot 1 paper. It tests Number System. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The remainder, when $(15^{23} + 23^{23})$ is divided by $19$ , is:

A.
$4$
B.
$15$
C.
$0$
D.
$18$

Answer

Explanation

Note that $15 \equiv -4 \pmod{19}$ and $23 \equiv 4 \pmod{19}$ . Therefore: $15^{23} + 23^{23} \equiv (-4)^{23} + 4^{23} \equiv -4^{23} + 4^{23} \equiv 0 \pmod{19}$ Hence, the remainder is $0$ .

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Remainder of Exponential Sum

Explanation

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