MathDB

3

Part of 2016 European Mathematical Cup

Problems(2)

European Mathematical Cup 2016 problem 3 senior division

Source:

12/31/2016
Determine all functions f:Rā†’Rf:\mathbb R\to\mathbb R such that equality f(x+y+yf(x))=f(x)+f(y)+xf(y)f(x + y + yf(x)) = f(x) + f(y) + xf(y) holds for all real numbers xx, yy.
Proposed by Athanasios Kontogeorgis
algebra
European Mathematical Cup 2016 junior division problem 3

Source:

12/31/2016
Prove that for all positive integers nn there exist nn distinct, positive rational numbers with sum of their squares equal to nn.
Proposed by Daniyar Aubekerov
number theory