Thread: natural number problem

Let A and B be two Natural Numbers. Suppose the remainder when A is divided by n is a and the remainder when B is divided by n is b. How does the remainder when A x B is divided by n compare to the remainders a and b? Can the remainder of A x B divided by n be determined by just considering a and b? If so, prove your theory.

Thanks!!

Originally Posted by kelly1183

Let A and B be two Natural Numbers. Suppose the remainder when A is divided by n is a and the remainder when B is divided by n is b. How does the remainder when A x B is divided by n compare to the remainders a and b? Can the remainder of A x B divided by n be determined by just considering a and b? If so, prove your theory.

Thanks!!

Symbolically,





The answer is known to be



To prove, just write




and expand the product .