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

6 The integers [2.0.1] Example: Let pbe a prime number. We claim that there is no p pin the rationals Q . Suppose, to the contrary, that a=b= p p. Without loss of ... - Read more

a b (mod m); a is congruent to b modulo m ... A positive integer p is prime if the ... Let a and b be positive integers. - Read more

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

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I need some help with this problem If a,b are integers such that a congruent b mod p for every positive prime p, prove that a=b.

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Math 580/780I Notes 5 Modular Arithmetic: Deﬁnition. Two integers a and b are congruent modulo an integer n if nj(a b). Notation. a b (mod n).

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