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x^2_{n+1}= ax_nx_{n+1} + bx^2_n

Source: 2019 Ecuador Juniors (OMEC) L2 p6

October 24, 2022
recurrence relationalgebra

Problem Statement

Let x0,a,bx_0, a, b be reals given such that b>0b > 0 and x0≠0x_0 \ne 0. For every nonnegative integer nn a real value xn+1x_{n+1} is chosen that satisfies xn+12=axnxn+1+bxn2.x^2_{n+1}= ax_nx_{n+1} + bx^2_n . a) Find how many different values xnx_n can take. b) Find the sum of all possible values of xnx_n with repetitions as a function of n,x0,a,bn, x_0, a, b.
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