Abstract
For each integer [Formula: see text], let [Formula: see text] denote the generalized [Formula: see text]-gonal number [Formula: see text] with [Formula: see text]. Given positive integers [Formula: see text] and an odd prime number [Formula: see text] with [Formula: see text], we employ the theory of ternary quadratic forms to determine completely when the mixed sum [Formula: see text] represents all but finitely many positive integers.
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