Modulus of a Product

If you have the product of two numbers and want to calculate the modulus of said product

  Where A,B and C are integers

let  where a & b are the modulus of A & B respectively and m & n are integers

Substituting:

 and because everything is an integer

  and thus

 since a & b are already the modulus of A & B. Now if this product is larger than C the modulus function will need be reapplied as in the following example:

Example:  A=8 B=8 C=5

   which is the same as above