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sqrt{x^3 + y^3 + z^3}=1969 has no solutions.

Source:

September 29, 2010
modular arithmeticnumber theoryDiophantine equationAdditive Number Theoryperfect cubeIMO ShortlistIMO Longlist

Problem Statement

(BUL1)(BUL 1) Prove that the equation x3+y3+z3=1969\sqrt{x^3 + y^3 + z^3}=1969 has no integral solutions.
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