MathDB

5

Part of 2021 New Zealand MO

Problems(2)

DE//AB wanted, isosceles ABC, BE=CD NZMO 2021 R1 p5

Source:

9/20/2021
Let ABCABC be an isosceles triangle with AB=ACAB = AC. Point DD lies on side ACAC such that BDBD is the angle bisector of ∠ABC\angle ABC. Point EE lies on side BCBC between BB and CC such that BE=CDBE = CD. Prove that DEDE is parallel to ABAB.
parallelogramisoscelesgeometry
y^5 + 2xy = x^2 + 2y^4

Source: New Zealand MO 2021 Round 2 p5 NZMO

10/6/2021
Find all pairs of integers x,yx, y such that y5+2xy=x2+2y4.y^5 + 2xy = x^2 + 2y^4. .
Diophantine equationnumber theorydiophantine