lean_workbook_plus_5612

Given positive integers $a,b,n$ such that $\gcd(a,n) = \gcd(b,n) = 1$ . Show these statements: (1): there exist a positive integer $t$ , such that $a^{t}\equiv\ b^{t} \pmod n$ . (2): if $d$ is a smallest positive integer such that $a^{d}\equiv\ b^{d} \pmod n$ , then $d|t$ for any such $t$ . (3): $3^n-2^n$ is not divisible by $n$ , for any natural number $n>1$ .