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Centroamerican Math Olympiad - 2017 P2

Source: OMCC 2017

June 23, 2017
OMCCOMCC 2017CENTROalgebranumber theory

Problem Statement

We call a pair (a,b)(a,b) of positive integers, a<391a<391, pupusa if
lcm(a,b)>lcm(a,391)\textup{lcm}(a,b)>\textup{lcm}(a,391)
Find the minimum value of bb across all pupusa pairs.
Fun Fact: OMCC 2017 was held in El Salvador. Pupusa is their national dish. It is a corn tortilla filled with cheese, meat, etc.
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