MathDB
Equation with Floor

Source: 2012 Baltic Way, Problem 3

November 22, 2012
floor functionalgebra unsolvedalgebra

Problem Statement

(a) Show that the equation ⌊x⌋(x2+1)=x3,\lfloor x \rfloor (x^2 + 1) = x^3, where ⌊x⌋\lfloor x \rfloor denotes the largest integer not larger than xx, has exactly one real solution in each interval between consecutive positive integers.
(b) Show that none of the positive real solutions of this equation is rational.
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