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Representation of Integers as Sums of Fibonacci and Lucas Numbers
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Motivated by the Elementary Problem B-416 in the Fibonacci Quarterly, we show that, given any integers n and r with n≥2, every positive integer can be expressed as a sum of Fibonacci numbers whose indices are distinct integers not congruent to r modulo n. Similar expressions are also dealt with for the case of Lucas numbers. Symmetric and anti-symmetric properties of Fibonacci and Lucas numbers are used in the proofs.
Title: Representation of Integers as Sums of Fibonacci and Lucas Numbers
Description:
Motivated by the Elementary Problem B-416 in the Fibonacci Quarterly, we show that, given any integers n and r with n≥2, every positive integer can be expressed as a sum of Fibonacci numbers whose indices are distinct integers not congruent to r modulo n.
Similar expressions are also dealt with for the case of Lucas numbers.
Symmetric and anti-symmetric properties of Fibonacci and Lucas numbers are used in the proofs.
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More on the Fascinating Characterizations of Mulatu’s Numbers
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Background
The discoveries of Mulatu’s numbers, better known as Mulatu’s sequence, represent revolutionary contributions to the mathematical world. His best-known...
More on the Fascinating Characterizations of Mulatu’s Numbers
More on the Fascinating Characterizations of Mulatu’s Numbers
Background The discoveries of Mulatu’s numbers, better known as Mulatu’s sequence, represent revolutionary contributions to the mathematical world. His best-known work is Mulatu’s ...
More on the Fascinating Characterizations of Mulatu’s Numbers
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Background The discoveries of Mulatu’s numbers, better known as Mulatu’s sequence, represent revolutionary contributions to the mathematical world. His best-known work is Mulatu’s ...