MathDB

3

Part of 2017 CentroAmerican

Problems(2)

Centroamerican Math Olympiad 2017 - P3

Source:

6/23/2017
Let ABCABC be a triangle and DD be the foot of the altitude from AA. Let ll be the line that passes through the midpoints of BCBC and ACAC. EE is the reflection of DD over ll. Prove that the circumcentre of △ABC\triangle ABC lies on the line AEAE.
OMCCOMCC 2017CENTROgeometrygeometric transformationreflectioncircumcircle
Centroamerican Math Olympiad 2017 - P6

Source: OMCC 2017

6/23/2017
Tita the Frog sits on the number line. She is initially on the integer number k>1k>1. If she is sitting on the number nn, she hops to the number f(n)+g(n)f(n)+g(n), where f(n)f(n) and g(n)g(n) are, respectively, the biggest and smallest positive prime numbers that divide nn. Find all values of kk such that Tita can hop to infinitely many distinct integers.
OMCCOMCC 2017CENTROnumber theoryprime numbers