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Find the remainder when 100^100 is divided by 7

 May 12, 2017
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Find the remainder when 100^100 is divided by 7

 

100100(mod7)|1002(mod7)2100(mod7)|because gcd(2,7)=1 :|2ϕ(7)1(mod7)ϕ(7)=6ϕ() is the Euler's totient function|261(mod7)2100(mod7)|100=616+42616+4(mod7)(26)1624(mod7)11624(mod7)24(mod7)16(mod7)2(mod7)

 

 

laugh

 May 12, 2017
edited by heureka  May 12, 2017
edited by heureka  May 12, 2017

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