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papacy
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Homework Statement
Find the smallest natural number n such that: a^(3n)=a (mod 85) for each integer a.
Justify your answer.
Homework Equations
The Attempt at a Solution
because 85=17 . 5 and gcd (5,17)=1 we have to find the n such:
a^(3n)=a (mod 5) and a^(3n)=a (mod 17).
From Fermat theorem we know that a^(17)=a (mod 17) and a^(5)=a (mod 5)
so we have: a^(5)=a^(3n) (mod 5) and a^(17)=a^(3n)(mod 17).
I don't now how to continue and find the smallest natural n.