Latest CAT Aptitude Question SOLUTION: The remainder when (15^23+23^23) is divided by 19 is (1)4 (2)15 (3)0 (4)18

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(#M40010193) CAT question Keep an EYE

The remainder when (15^23+23^23) is divided by 19 is
(1)4 (2)15 (3)0 (4)18

Asked In CAT prashanthi (11 years ago)

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phani  (11 years ago)

(19-4)^23+(19+4)^23
the remainder is 0.
(19-4)^23 expansion all are multiplied by 19 except last term -4^23
(19+4)^23 expansion all are multiplied by 19 except last term 4^23( as per principle of binomial theorem..............it is difficult to type)
adding both we get 0

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atulya kant  (11 years ago)

(a^n+b^n) when divided by a+b leaves no remainder, if n is odd
here also n=23(odd) so 15+23 will completely divide the sum nd so will 19

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