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Positive integers of the form 2x² - 3y² and 10xy - x² - y².

Source: Tuymaada 2003, day 2, problem 2.

May 5, 2007

modular arithmeticnumber theory proposednumber theory

Problem Statement

Which number is bigger : the number of positive integers not exceeding 1000000 that can be represented by the form

2x^{2}-3y^{2}

with integral

x

and

y

or that of positive integers not exceeding 1000000 that can be represented by the form

10xy-x^{2}-y^{2}

with integral

x

and

y?

Proposed by A. Golovanov