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The greatest square free factor of a binary recursive sequence

Abstract : If $\Delta_{m,n}$ denotes the quotient $[u_m,v_n]/(u_m,v_n)$ of the lcm by the gcd, we obtain in this paper a lower bound for the greatest square-free factor $Q[\Delta_{m,n}]$ of $\Delta_{m,n}$ when $u_h=v_h, m>n$ (and $u_n\neq0$); this implies a lower bound for $\log Q[u_n]$ of the form $C(\log m)^2(\log\log m)^{-1}$, thereby improving on an earlier result of C. L. Stewart.
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Tarlok Nath Shorey. The greatest square free factor of a binary recursive sequence. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1983, Volume 6 - 1983, pp.23 - 36. ⟨10.46298/hrj.1983.97⟩. ⟨hal-01104239⟩

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