MathDB

1

Part of 1991 Bundeswettbewerb Mathematik

Problems(2)

product of 1991 numbers >1 if product of any 10 is >1

Source: 1991 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p1

11/20/2022
Given 19911991 distinct positive real numbers, the product of any ten of these numbers is always greater than 11. Prove that the product of all 19911991 numbers is also greater than 11.
algebrainequalitiesProduct
4^x + 4^y + 4^z = u^2

Source: 1991 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p1

11/20/2022
Determine all solutions of the equation 4x+4y+4z=u24^x + 4^y + 4^z = u^2 for integers x,y,zx,y,z and uu.
number theoryPerfect SquaresDiophantine equationdiophantine