Let n=391=17*23. Show that 2n-11 (mod n). Find an exponent j>0 such that
2j1 (mod n)
Use Euler's theorem, which states that for any integer , relatively prime to ,
where is Euler's phi function.
So, by Euler's theorem, with , you have .
For the first part you can use the Chinese Remainder Theorem. You have :
so it's impossible that .
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