On a Diophantine equation involving powers of Fibonacci numbers
This paper deals with the diophantine equation F-1(p) + 2F(2)(p )+ . . . + kF(k)(p) = F-n(q), an equation on the weighted power terms of Fibonacci sequence. For the exponents p, q is an element of {1, 2} the problem has already been solved in ad hoc ways using the properties of the summatory identit...
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| Main Authors: | , , |
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| Format: | Article |
| Published: |
2020
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| Series: | PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES
96 No. 4 |
| Subjects: | |
| Online Access: | http://publicatio.uni-sopron.hu/1946 |
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| Summary: | This paper deals with the diophantine equation F-1(p) + 2F(2)(p )+ . . . + kF(k)(p) = F-n(q), an equation on the weighted power terms of Fibonacci sequence. For the exponents p, q is an element of {1, 2} the problem has already been solved in ad hoc ways using the properties of the summatory identities appear on the left-hand side of the equation. Here we suggest a uniform treatment for arbitrary positive integers p and q which works, in practice, for small values. We obtained all the solutions for p, q <= 10 by testing the new approach. |
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| Physical Description: | 33-37 |
| ISSN: | 0386-2194 |