Question: Show that if we do all arithmetic modulo a prime number, p, then, for any integer x > 0, {ix mod p: i = 0,

Show that if we do all arithmetic modulo a prime number, p, then, for any integer x > 0, 

{ix mod p: i = 0, 1,...,p − 1} = {i : i = 0, 1,...,p − 1}. 

Use the fact that if p is prime, then every nonzero integer less than p has a multiplicative inverse when we do arithmetic modulo p.

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