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Piotr
Posts:
2
Registered:
9/19/12


Re: I need to demonstrate that 3^80 2^20 is divisible by 5 . hint u(3^80)=1
Posted:
Oct 5, 2012 4:13 PM


3^80 2^20 is divisible by 5 if
3^80 = 2^20 (mod 5)
now observe that:
k  natural
(3^i) mod 5 = [nb you can call this function u] 1 for i=4k 3 for i=4k+1 4 for i=4k+2 2 for i=4k+3
and
(2^i) mod 5 =
1 for i=4k 2 for i=4k+1 4 for i=4k+2 3 for i=4k+3
so
(3^80) mod 5 = (3^(4*20+0)) mod 5 = 1 (2^20) mod 5 = (2^(4*5+0)) mod 5 = 1
and we are done



