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ax^2+bxy+cy^2 that are good

Source: IZHO 2023 / P5

February 5, 2023
number theory

Problem Statement

We call a positive integer nn is goodgood , if there exist integers a,b,c,x,ya,b,c,x,y such that n=ax2+bxy+cy2n=ax^2+bxy+cy^2 and b2−4ac=−20b^2-4ac=-20. Prove that the product of any two good numbers is also a good number.
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