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The remainder when 19200 23200 is divided by 49 is : null (Mathematics) | DivineJEE

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Mathematics

Exam

Mathematics

The remainder, when $19^{200}+23^{200}$ is divided by 49 , is ___________.

Correct Answer:

29

Explanation

19^{200}+23^{200}

=

(21-2)^{200}+(21+2)^{200}=49 \lambda+2^{201}

Now,

2^{201}=8^{67}=(7+1)^{67}=49 \lambda+7 \times 67+1

=49 \lambda+470

=49(\lambda+9)+29

\therefore

Remainder

=29

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