Remainder of Exponential Sum

CAT 2004 Slot 1 · QA · Easy · Number System

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The remainder, when (1523+2323)(15^{23} + 23^{23}) is divided by 1919, is:

  1. A.

    44

  2. B.

    1515

  3. C.

    00

  4. D.

    1818

Answer

C

Explanation

Note that 15≡−4(mod19)15 \equiv -4 \pmod{19} and 23≡4(mod19)23 \equiv 4 \pmod{19}. Therefore: 1523+2323≡(−4)23+423≡−423+423≡0(mod19)15^{23} + 23^{23} \equiv (-4)^{23} + 4^{23} \equiv -4^{23} + 4^{23} \equiv 0 \pmod{19} Hence, the remainder is 00.

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