Simultaneous Solution for Two Modular Equations with Known Integers

[mohamed el teir]

let equation 1: x % n1 = 0, equation 2: x % n2 =1, where n1 and n2 are known positive integers, any multiple of n1 will solve eqn1 and any multiple of n2 (and adding 1 to the multiple) will solve eqn2, but is there a short way to simultaneously solve the two equations to find x instead of continuously trying to find the first multiple of n2 that if 1 is added to it will be a multiple of n1 ?

 

[mfb]

The existence is given by the Chinese remainder theorem and the article describes some methods to find such a number.