MathDB

3

Part of 2017 Czech-Polish-Slovak Junior Match

Problems(2)

(x^2 + 1)(y^2 + 1) >= 2(xy - 1)(x + y)

Source: Czech-Polish-Slovak Junior Match 2017, individual p3 CPSJ

2/20/2020
Prove that for all real numbers x,yx, y holds (x2+1)(y2+1)≥2(xy−1)(x+y)(x^2 + 1)(y^2 + 1) \ge 2(xy - 1)(x + y). For which integers x,yx, y does equality occur?
inequalitiesalgebra
number of 8-digit numbers *2*0*1*7, divisible by 7

Source: Czech-Polish-Slovak Junior Match 2017, Team p3 CPSJ

3/6/2020
How many 88-digit numbers are ∗2∗0∗1∗7*2*0*1*7, where four unknown numbers are replaced by stars, which are divisible by 77?
Digitdivisiblenumber theory