On Amicable Numbers With Different Parity
Abstract
Description
In this paper we provide a straightforward proof that if a pair of amicable numbers with different parity exists (one number odd and the other one even), then the odd amicable number must be a perfect square, while the even amicable number has to be equal to the product of a power of 2 and an odd perfect square.
Plain LaTeX, 7 pages. This paper was submitted to the American Mathematical Monthly. AMM was not able to accept it since, amazingly enough, the same result was published by A. A. Gioia in the Monthly nearly forty years before (Vol. 74, No. 8, Oct., 1967)
Plain LaTeX, 7 pages. This paper was submitted to the American Mathematical Monthly. AMM was not able to accept it since, amazingly enough, the same result was published by A. A. Gioia in the Monthly nearly forty years before (Vol. 74, No. 8, Oct., 1967)