MathDB
1/(b-c)^2 +1/(c-a)^2 +1/(a-b)^2 is square of a rational for rational a,b,c

Source: 1976 Swedish Mathematical Competition p3

March 26, 2021
algebraPerfect Squarerational

Problem Statement

If aa, bb, cc are rational, show that 1(b−c)2+1(c−a)2+1(a−b)2 \frac{1}{(b-c)^2}+\frac{1}{(c-a)^2}+\frac{1}{(a-b)^2} is the square of a rational.
Back to ProblemsView on AoPS