MathDB

3

Part of 2017 Bosnia And Herzegovina - Regional Olympiad

Problems(3)

Regional Olympiad - FBH 2017 Grade 10 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

9/19/2018
Find prime numbers pp, qq, rr and ss, pairwise distinct, such that their sum is prime number and numbers p2+qrp^2+qr and p2+qsp^2+qs are perfect squares
number theoryprime numbers
Regional Olympiad - FBH 2017 Grade 9 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

9/19/2018
Does there exist positive integer nn such that sum of all digits of number n(4n+1)n(4n+1) is equal to 20172017
Digitsnumber theory
Regional Olympiad - FBH 2017 Grade 11 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

9/19/2018
Let SS be a set of 66 positive real numbers such that (a,b∈S)(a>b)⇒a+b∈S\left(a,b \in S \right) \left(a>b \right) \Rightarrow a+b \in S or a−b∈Sa-b \in S Prove that if we sort these numbers in ascending order, then they form an arithmetic progression
Arithmetic ProgressionSetsnumber theory