MathDB

2

Part of 2016 Czech-Polish-Slovak Junior Match

Problems(2)

if x^2 + y^2 - 1 < xy then x + y - |x - y| < 2

Source: Czech-Polish-Slovak Junior Match 2016, individual p2 CPSJ

1/20/2020
Let xx and yy be real numbers such that x2+y2−1<xyx^2 + y^2 - 1 < xy. Prove that x+y−∣x−y∣<2x + y - |x - y| < 2.
Slovakia
inequalitiesalgebra
max d, divides all 3 of abc, bca, cab where a,b,c non zero diff. digits

Source: Czech-Polish-Slovak Junior Match 2016, team p2 CPSJ

1/20/2020
Find the largest integer dd divides all three numbers abc,bcaabc, bca and cabcab with a,ba, b and cc being some nonzero and mutually different digits.
Czech Republic
number theorydividesDigits