remainder and fermat theorem

find the remainder when when 37^47 is divided by 7

1 5 2 4

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2 solutions

Elmer Rodriguez
Jun 3, 2020

I answered it using the Fermat's little Theorem....(37^6)^7•2^5÷7=1^42•2^5÷7=32÷7=4

Dmitry Lebedev
Oct 11, 2019

3 7 47 ( m o d 7 ) 2 47 ( m o d 7 ) 8 15 4 ( m o d 7 ) 4 . 37^{47} (mod 7) ≡ 2^{47} (mod 7) ≡ 8^{15}•4 (mod 7) ≡ \boxed{4}.

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