MathDB

4

Part of 2021 Czech-Polish-Slovak Junior Match

Problems(2)

min of x^4 + y^4 - x^2y - xy^2 when x,y>0 and x + y <= 1

Source: Czech-Polish-Slovak Match Junior 2021, individual p4 CPSJ

9/12/2021
Find the smallest value that the expression takes x4+y4−x2y−xy2x^4 + y^4 - x^2y - xy^2, for positive numbers xx and yy satisfying x+y≤1x + y \le 1.
algebrainequalities
2 different numbers with product perfect square from {70, 71, 72,... 70 + n}

Source: 2021 Czech-Polish-Slovak Match Junior, team p4 CPSJ

9/12/2021
Find the smallest positive integer nn with the property that in the set {70,71,72,...70+n}\{70, 71, 72,... 70 + n\} you can choose two different numbers whose product is the square of an integer.
number theoryPerfect Square