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2018-2019 Fall OMO Problem 12

Source:

November 7, 2018
Online Math Open

Problem Statement

Three non-collinear lattice points A,B,CA,B,C lie on the plane 1+3x+5y+7z=01+3x+5y+7z=0. The minimal possible area of triangle ABCABC can be expressed as mn\frac{\sqrt{m}}{n} where m,nm,n are positive integers such that there does not exists a prime pp dividing nn with p2p^2 dividing mm. Compute 100m+n100m+n.
Proposed by Yannick Yao
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