MathDB

2

Part of 2016 Bosnia And Herzegovina - Regional Olympiad

Problems(4)

Regional Olympiad - FBH 2016 Grade 9 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016

9/22/2018
Let ABCABC be an isosceles triangle such that ∠BAC=100∘\angle BAC = 100^{\circ}. Let DD be an intersection point of angle bisector of ∠ABC\angle ABC and side ACAC, prove that AD+DB=BCAD+DB=BC
geometryangle bisector
Regional Olympiad - FBH 2016 Grade 10 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016

9/22/2018
Let aa and bb be two positive integers such that 2ab2ab divides a2+b2−aa^2+b^2-a. Prove that aa is perfect square
number theoryDivisibilityFBHPerfect Square
Regional Olympiad - FBH 2016 Grade 11 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016

9/22/2018
Does there exist a right angled triangle, which hypotenuse is 201620172016^{2017} and two other sides positive integers.
geometrynumber theory
Regional Olympiad - FBH 2016 Grade 12 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016

9/22/2018
Find all elements n∈A={2,3,...,2016}⊂Nn \in A = \{2,3,...,2016\} \subset \mathbb{N} such that: every number m∈Am \in A smaller than nn, and coprime with nn, must be a prime number
combinatoricsCombinatorial Number Theorycoprimeset