A conversation at the Brilliant water cooler

Logic Level 3

Suyeon is thinking of 2 (not necessarily distinct) positive integers, xx and yy, each of which is greater than 1. She tells Calvin the product P=xyP = xy and Aaron the sum S=x+y.S = x + y. The equally intelligent Calvin and Aaron then engage in a short discussion as follows:

  • Calvin: "I cannot determine SS at this point."

  • Aaron: "All right then, here's a hint; SS does not exceed 2020, and if that's all you need to know to uniquely determine SS then I will know what PP is."

  • Calvin: "O.k., based solely on the fact that SS does not exceed 2020 I am now able to uniquely determine SS."

Find S+PS + P.

This question was inspired by the long-suffering Calvin Lin (inside joke).

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