(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

Let a, b, s, t be integers with s, t > 0. What conditions must s, t satisfy if the following statement is true:

If a = b (mod s) and a = b (mod t), then a = b (mod st).

The attempt at a solution

If s | a, s | b, t | a and t | b, then st | a and st | b if and only if s, t are relatively prime. This is as far as I've gone. How should I continue?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: A Modular Arithmetic Proof Problem

**Physics Forums | Science Articles, Homework Help, Discussion**