MathDB
2021 Spring LMT Division A Problem 25, B Problem 26

Source:

January 22, 2022
number theory

Problem Statement

Chandler the Octopus is making a concoction to create the perfect ink. He adds 1.21.2 grams of melanin, 4.24.2 grams of enzymes, and 6.66.6 grams of polysaccharides. But Chandler accidentally added n grams of an extra ingredient to the concoction, Chemical XX, to create glue. Given that Chemical XX contains none of the three aforementioned ingredients, and the percentages of melanin, enzymes, and polysaccharides in the final concoction are all integers, find the sum of all possible positive integer values of nn.
Proposed by Taiki Aiba