MathDB

2

Part of 2018 Bosnia And Herzegovina - Regional Olympiad

Problems(3)

Regional Olympiad - FBH 2018 Grade 9 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2018

9/18/2018
Determine all triplets (a,b,c)(a,b,c) of real numbers such that sets {a2−4c,b2−2a,c2−2b}\{a^2-4c, b^2-2a, c^2-2b \} and {a−c,b−4c,a+b}\{a-c,b-4c,a+b\} are equal and 2a+2b+6=5c2a+2b+6=5c. In every set all elements are pairwise distinct
number theorySetsequal sets
Regional Olympiad - FBH 2018 Grade 10 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2018

9/18/2018
Find all positive integers nn such that number n4−4n3+22n2−36n+18n^4-4n^3+22n^2-36n+18 is perfect square of positive integer
IntegerPerfect Squaresnumber theory
Regional Olympiad - FBH 2018 Grade 11 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2018

9/18/2018
Let a1,a2,...,a2018a_1, a_2,...,a_{2018} be a sequence of numbers such that all its elements are elements of a set {−1,1}\{-1,1\}. Sum S=∑1≤i<j≤2018aiajS=\sum \limits_{1 \leq i < j \leq 2018} a_i a_j can be negative and can also be positive. Find the minimal value of this sum
SumSequencealgebra