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International Journal of Mathematics and Mathematical Sciences
Volume 14, Issue 4, Pages 697-703

Lucas numbers of the form PX2, where P is prime

Mathematics Dept., San Francisco State University, San Francisco 94132, CA, USA

Received 1 February 1989; Revised 8 February 1990

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let Ln denote the nth Lucas number, where n is a natural number. Using elementary techniques, we find all solutions of the equation: Ln=px2 where p is prime and p<1000.