Volume 12 ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4
On some solved and unsolved problems related to Egyptian unit fractions
Original research paper. Pages 1–7
Peter Vassilev and Mladen Vassilev-Missana
Full paper (99 Kb) | Abstract
In the paper a method named “Continuation of Unity” that is very useful for obtaining infinitely many decompositions of the number 1 with the help of Unit Egyptian fractions starting from given initial decomposition is demonstrated. The important question about decompositions of the number 1 with the help of unit fractions with distinct denominators that belong to a fixed increasing arithmetic progression of natural numbers is discussed. Also some applications related to fractions with odd denominators only are proposed.
Lucas’ theorem for extended generalized binomial coefficients
Original research paper. Pages 8–12
R. L. Ollerton and A. G. Shannon
Full paper (39 Kb)
An extremal problem related to the Fibonacci sequence
Original research paper. Pages 13–20
K. T. Atanassov, R. D. Knott, R. L. Ollerton and A. G. Shannon
Full paper (58 Kb) | Abstract
This paper continues our study of Fibonacci inequalities. For the set An = {Fn−1, 4Fn−2, …, (n−2)2F2} with kth element given by ak = k2Fn−k, it is proved that the unique maximal element is given by a* = a4 = 16Fn−4, n ≥ 9.
