- #1

dancergirlie

- 200

- 0

## Homework Statement

If a and b are integers and a is congruent to b(mod p) for every positive prime p, prove that a=b

## Homework Equations

p divides (a-b) if a is congruent to b modulo p

if p divides ab then p divides a or p divides b (if p is prime)

## The Attempt at a Solution

Suppose a is congruent to b(mod p)

so, p divides (a-b)

which means, there exists an integer c so that (a-b)=pc

where a=pc+b

(pc+b) is congruent to b(mod p)

so, p divides (pc+b-b)= (pc)

p divides (pc)

This is where i get stuck, i don't know if i should say since p is prime, p divides p or p divides c, or i don't know if i did this completely wrong. Any help would be appreciated =)