HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

# 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.
Keywords :
Document type :
Journal articles
Domain :
Complete list of metadata

Cited literature [5 references]

https://hal.archives-ouvertes.fr/hal-01104239
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Friday, January 16, 2015 - 1:54:32 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Friday, September 11, 2015 - 6:57:09 AM

### File

6Article2.pdf
Explicit agreement for this submission

### Citation

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⟩

Record views