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Source: Indian Postal Coaching 2005

October 27, 2005
inductionnumber theory unsolvednumber theory

Problem Statement

Let kk be an even positive integer and define a sequence <xn><x_n> by x1=1,xn+1=kxn+1. x_1= 1 , x_{n+1} = k^{x_n} +1. Show that xn2x_n ^2 divides xn−1xn+1x_{n-1}x_{n+1} for each n≥2.n \geq 2.
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