ON THE ADDITION OF VALUES OF A QUADRATIC POLYNOMIAL AT UNITS MODULO n

Let Z(n) be the ring of residue classes modulo n, Z(n)* be its unit group, and let f(z) = az(2) + bz be an integral quadratic polynomial with b not equal 0 and gcd(a, b) = 1. In this paper, for any integer c and positive integer n we give a formula for the number of solutions of the congruence equation f(x) + f(y) equivalent to c (mod n) with x, y units (mod n). This partly solves a problem posed by Yang and Tang in [11].