Prime Product Modulus: Solve by Modular Arithmetic

Does a product of primes divide an expression?

We justified our steps with a discussion of Euler's phi function and Fermat's little theorem.

To clarify, if we consider all of the integers, and then if we perform mod 5, then all of those integers are congruent to 0, 1, 2, 3, 4 (mod5). Which applies to (0, 1, 2...n-1) (modn).

Sources:

Socratica - YT Channel
W. Sierpinski - Problems in Number Theory, Polish Academy of Sciences, 1970; problem 7