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a,b,c are not triangle sidelengths when c is a perfect square, a,b>1000

Source: Caucasus 2015 11.5

April 26, 2019
number theoryPerfect SquareSides of a triangle

Problem Statement

Are there natural a,b>1000a, b >1000 , such that for any cc that is a perfect square, the three numbers a,ba, b and cc are not the lengths of the sides of a triangle?
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