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Let k be a fixed integer greater than 1, and let {m=4k^2-5}. Show that there exist positive integers a and b such that the sequence (x_n) defined by x_0=a,\quad x_1=b,\quad x_{n+2}=x_{n+1}+x_n\quad\text{for}\quad n=0,1,2,\dots has all of its terms relatively prime to m.

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