Almost universal mixed sums of squares and polygonal numbers.

For each integer m ≥ 3 , let P m (x) denote the generalized m -gonal number (m − 2) x 2 − (m − 4) x 2 with x ∈ ℤ. Given positive integers a , b , c , k and an odd prime number p with p ∤ c , we employ the theory of ternary quadratic forms to determine completely when the mixed sum a x 2 + b y 2 + c P p k + 2 (z) represents all but finitely many positive integers. [ABSTRACT FROM AUTHOR]