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ASU 301 All Soviet Union MO 1980 [x^3/2]r +[y^3/2]=B has 1980 int. solutions

Source:

July 19, 2019
floor functionalgebraequation

Problem Statement

Prove that there is an infinite number of such numbers BB that the equation ⌊x3/2⌋+⌊y3/2⌋=B\lfloor x^3/2\rfloor + \lfloor y^3/2 \rfloor = B has at least 19801980 integer solutions (x,y)(x,y).
(⌊z⌋\lfloor z\rfloor denotes the greatest integer not exceeding zz.)
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