Reminding a Remainder

The remainder when ( 2345 ) 678 + ( 1234 ) 567 (2345)^{678}+(1234)^{567} is divided by 4 is :-


The answer is 1.

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1 solution

Parag Zode
Dec 25, 2014

( 2345 ) 678 = ( 2344 + 1 ) 678 = 4 k + 1 (2345)^{678}=(2344+1)^{678}=4k+1 and we see that ( 1234 ) 567 (1234)^{567} is divisible by 4. Hence the remainder is 1 \boxed{1}

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