MathDB
2021 LMT Spring Division A Problem 19

Source:

October 22, 2021

Problem Statement

Let SS be the sum of all possible values of a⋅ca \cdot c such that a3+3ab2−72ab+432a=4c3a^3+3ab^2-72ab+432a=4c^3 if aa, bb, and cc are positive integers, a+b>11a+b > 11, a>b−13a > b-13, and c≤1000c \le 1000. Find the sum of all distinct prime factors of SS.
Proposed by Kevin Zhao
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