amicable numbers

A rational amicable pair consists of two integers a and b for which the divisor functions are equal and are of the form σ(a) = σ(b) = (P(a, b))/(Q(a, b)) congruent R(a, b), where P(a, b) and Q(a, b) are bivariate polynomials, and for which the following properties hold (Y. Kohmoto): 1. All the degrees of terms of the numerator of the right fraction are the same. 2. All the degrees of terms of the denominator of the right fraction are the same. 3. The degree of P is one greater than the degree of Q.