AMC / AIME · Modular Arithmetic · AIME / USAJMO / AMO

Modular Arithmetic: (Proof track.) Prove that the order of math modulo math (when math) divides math. Enter the order of math modulo math.

Congruences and power cycles.

Try the problem

**(Proof track.)** Prove that the order of

a

modulo

n

(when

\gcd(a,n)=1

) divides

\varphi(n)

. Enter the order of

3

modulo

14

Orders and Fermat.

\varphi(14)=6

; check minimal.