Calculators Forbidden - 2

Find the remainder when 16^7 is divided by 42 .


The answer is 16.

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1 solution

Kay Xspre
Dec 3, 2015

As 2 7 = 3 ( 42 ) + 2 2^7=3(42)+2 , therefore ( 2 7 ) 4 = ( 3 ( 42 ) + 2 ) 4 (2^7)^4 = (3(42)+2)^4 . The binomial expansion will result into all terms except the last ( 16 ) (16) being divided by 42, thus, 1 6 7 16 ( m o d 42 ) 16^7\equiv 16\pmod{42}

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