Answer to Question #95981 in Algebra for Bsaad Abdul Aziz

Question

Show that numbers of the form a squared plus b squared, where a and b are integers are closed Under multiplication

Answer 1

Suppose that the given numbers a and b are fractional, then will be fractional a squared and b squared.

 Therefore, their sum is also a fractional number.

The operation of the product of fractional numbers will also return the result to the set of fractional numbers. If one sets denominators to be equal to 1, then one gets integer numbers.

The initial variables are integer if and only if the result is also integer.