MathDB

1

Part of 2012 Spain Mathematical Olympiad

Problems(2)

Can 3n^2+2n+2 be a square?

Source: Spanish MO 2012 Q1

6/7/2012
Determine if the number λn=3n2+2n+2\lambda_n=\sqrt{3n^2+2n+2} is irrational for all non-negative integers nn.
number theory proposednumber theory
Diophantine for n and k

Source: Spanish MO 2012 Q4

6/7/2012
Find all positive integers nn and kk such that (n+1)n=2nk+3n+1(n+1)^n=2n^k+3n+1.
modular arithmeticinequalitiesnumber theory proposednumber theory