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3/4 =1/a+1/b+1/c diophantine

Source: Chile Finals 2011 L2 p1

October 5, 2022
number theorydiophantineDiophantine equation

Problem Statement

Find all the solutions (a,b,c)(a, b, c) in the natural numbers, verifying 1≤a≤b≤c1\le a \le b \le c, of the equation34=1a+1b+1c.\frac34=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}.
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