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1

Part of 2014 Gulf Math Olympiad

Problems(1)

GMO 2014 #1

Source: GMO 2014

9/21/2017
A sequence a0,a1,a2,⋯a_0,a_1,a_2,\cdots satisfies the conditions a0=0a_0 = 0 , an−12−an−1=an2+ana_{n-1}^2 - a_{n-1} = a_n^2 + a_n 1) determine the two possible values of a1a_1 . then determine all possible values of a2a_2 . 2)for each nn, prove that an+1=an+1a_{n+1}=a_n+1 or an+1=−ana_{n+1} = -a_n 3)Describe the possible values of a1435a_{1435} 4)Prove that the values that you got in (3) are correct
GMO-Gulf Mathmatical Olympiadalgebra