Chinese Remainder Theorem: When a divisor can be split into two co-prime factors a and b such that N = a x b , then by dividing the given number M with individual factors such that remainder in each case is p and q that is M mod a = p and M mod b = q and two variables are introduced and an equation is formed such that ax+by = 1, it is important to note that x and y can only take integral values. So after finding the individual remainders of M when divided by factors a and b, this equation is solved to get integral values of x and y.
Thus, the Chinese remainder states that
M mod N = (aqx+ bpy) mod N
Where a and b are factors of divisors and are co-prime
p and q are individual remainders when M is divided by a and b
M mod a = p and M mod b = q
x and y are integers that satisfy the equation ax+by = 1
