MathDB

3

Part of 2011 South East Mathematical Olympiad

Problems(2)

find all n

Source: China South East Mathematical Olympiad 2011

8/18/2011
Find all positive integer nn , such that for all 35-element-subsets of M=(1,2,3,...,50)M=(1,2,3,...,50) ,there exists at least two different elements a,ba,b , satisfing : a−b=na-b=n or a+b=na+b=n.
combinatorics proposedcombinatorics
sequence problem

Source: China South East Mathematical Olympiad 2011

8/18/2011
The sequence (an)n>=1(a_n)_{n>=1} satisfies that : a1=a2=1a_1=a_2=1 an=7an−1−an−2a_n=7a_{n-1}-a_{n-2} (n>=3n>=3) , prove that : for all positive integer n , number an+2+an+1a_n+2+a_{n+1} is a perfect square .
inductionalgebra proposedalgebra