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Number of triples (x,a,b)

Source: INMO Problem 3

January 15, 2017
algebrafloor function

Problem Statement

Find the number of triples (x,a,b)(x,a,b) where xx is a real number and a,ba,b belong to the set {1,2,3,4,5,6,7,8,9}\{1,2,3,4,5,6,7,8,9\} such that x2āˆ’a{x}+b=0.x^2-a\{x\}+b=0. where {x}\{x\} denotes the fractional part of the real number xx.
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