MathDB

301

Part of 1980 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

7/19/2019
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.)
floor functionalgebraequation