We prove that if a,b,c,d,e,m are integers, m > 0 and (m,ac) = 1, then there exist infinitely many positive integers n such that m|(an+b)cⁿ - deⁿ. Hence we derive a similar conclusion for ternary integral recurrences.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-3,
author = {A. Schinzel},
title = {On Ternary Integral Recurrences},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {63},
year = {2015},
pages = {19-23},
zbl = {06488953},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-3}
}
A. Schinzel. On Ternary Integral Recurrences. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) pp. 19-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-3/