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1/a+1/b+1/c=0 , gcd=1, no of triples with 50 \ge |a| \ge |b| \ge |c| 1

Source: Singapore Junior Math Olympiad 2017 2nd Round p5 SMO

March 26, 2020
number theorycombinatoricscoprime

Problem Statement

Let a,b,ca, b, c be nonzero integers, with 11 as their only positive common divisor, such that 1a+1b+1c=0\frac{1}{a}+\frac{1}{b}+\frac{1}{c}= 0. Find the number of such triples (a,b,c)(a, b, c) with 50≥∣a∣≥∣b∣≥∣c∣150 \ge |a| \ge |b| \ge |c| 1.
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