On Sums of Practical Numbers and Polygonal Numbers

Practical numbers are positive integers n such that every positive integer less than or equal to n can be written as a sum of distinct positive divisors of n. In this paper, we show that all positive integers can be written as a sum of a practical number and a triangular number, resolving a conjecture by Sun. We also show that all sufficiently large natural numbers can be written as a sum of a practical number and two s-gonal numbers.