MathDB

2

Part of 2009 Mathcenter Contest

Problems(2)

locus of P, ABCD square such that max { PA, PC\}=1/2(PB+PD)

Source: Mathcenter Contest / Oly - Thai Forum 2009 R1 p2 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

11/9/2022
Find the locus of points PP in the plane of a square ABCDABCD such that max⁡{PA, PC}=12(PB+PD).\max\{ PA,\ PC\}=\frac12(PB+PD).
(Anonymous314)
geometryLocussq
4ab/(ab^2+1) is a natural

Source: Mathcenter Contest / Oly - Thai Forum 2009 R2 p2 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

11/9/2022
Find all natural numbers that can be written in the form 4abab2+1\frac{4ab}{ab^2+1} for some natural a,ba,b.
(nooonuii)
number theory