Show that 70 divide 1016n−1 for all n natural numbers.
I tried to show that 1016n≡1 mod 70.
Thanks for all. I got it.
Note that 70 = 7.5.2
As 101ϕ(7) ≡1 mod 7, so 1016n ≡1 mod 7 (Euler Theorem)
and 101ϕ(2) ≡1 mod 2, so 1016n ≡1 mod 2 (Euler Theorem)
and 101 ≡1 mod 5, so 1016n ≡1 mod 5
Therefore, 1016n ≡1 mod 70.
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