MathDB

3

Part of 2019 Durer Math Competition Finals

Problems(3)

p^q + p^r is a perfect square, 3 primes related

Source: 2019 Dürer Math Competition Finals E1.3

11/28/2020
Determine all triples (p,q,r)(p, q, r) of prime numbers for which pq+prp^q + p^r is a perfect square.
Perfect Squarenumber theory
at most n true statements

Source: 2019 Dürer Math Competition Finals Day2 E3 https://artofproblemsolving.com/community/c1621835_2019_

1/5/2022
On a piece of paper we have 20192019 statements numbered from 11 to 20192019. The nthn^{th} statement is the following: "On this piece of paper there are at most nn true statements". How many of the statements are true?
combinatorics
min perimeter of ABC, if 6 cevians divide the sides into 6 integer lengths

Source: 2019 Dürer Math Competition Finals Day2 E+3 https://artofproblemsolving.com/community/c1621835_2019_

1/5/2022
Let PP be an interior point of triangle ABCABC. The lines APAP, BPBP and CPCP divide each of the three sides into two segments. If the so-obtained six segments all have distinct integer lengths, what is the minimum possible perimeter of ABCABC?
geometryperimeterGeometric Inequalities