Let a and b be two distinct prime numbers and x and y are integers. Is the following true?
(x≡ymoda) and (x≡ymodb). So, a|(x−y) and b|(x−y). This means x−y=abϕ with ϕ∈Z.
Can I state the last part or do I need to prove that somehow? It seems logical enough to me but it might be wrong. Your help is appreciated.
Answer
Let x−y=am=bn, m,n∈Z.
am=bn
Since a and b are coprime and a∣bn, a∣n. Let n=aϕ.
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