Ramanujan’s Ternary Quadratic Form

do not seem to obey any simple law.” Following I. Kaplansky, we call a non-negative integer N eligible for a ternary form f(x, y, z) if there are no congruence conditions prohibiting f from representing N. By the classical theory of quadratic forms, it is well known that any given genus of positive definite ternary quadratic forms represents every eligible integer. Consequently if a genus consists of a single class with representative f(x, y, z), then f represents every eligible integer. In the case of Ramanujan’s form, this only implies that an eligible integer, one not of the form 4(16μ+ 6), is represented by φ1 or φ2.