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Why gcd(i,p-1)=1 iff gcd(p-i,p-1)=1 ?

Quote: Originally Posted by userit8 Why gcd(i,p-1)=1 iff gcd(p-i,p-1)=1 ? p=13, i=5 gcd(5,12)=1, gcd(8,12)=4 ?