MathDB

5

Part of 2023 International Zhautykov Olympiad

Problems(1)

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

Source: IZHO 2023 / P5

2/5/2023
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.
number theory