Find the remainder when 16^7 is divided by 42 .
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As 2 7 = 3 ( 4 2 ) + 2 , therefore ( 2 7 ) 4 = ( 3 ( 4 2 ) + 2 ) 4 . The binomial expansion will result into all terms except the last ( 1 6 ) being divided by 42, thus, 1 6 7 ≡ 1 6 ( m o d 4 2 )