Even perfect numbers in Narayana's sequence
DOI:
https://doi.org/10.5269/bspm.70198Resumen
In this note we prove that 6 and 28 are the only perfect numbers present in Narayana’s sequence.
Referencias
1. Bravo, J.J. and Herrera, J. L., Even perfect numbers in generalized Pell sequences, Lith. Math. J. 61(1), 1-12, (2021).
2. Bravo, J.J. and Luca, F., Perfect Pell and Pell–Lucas numbers, Stud. Sci. Math. Hung. 56(4), 381-387, (2019).
3. Bugeaud, Y., Mignotte, M. and Siksek, S., Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers, Ann. Math. (2) 163, 969-1018, (2006).
4. Dujella, A. and Petho, A., A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. 49, 291-306, (1988).
5. Faco, V. and Marques, D., Even perfect numbers among generalized Fibonacci sequences, Rend. Circ. Mat. Palermo 63, 363-370, (2014).
6. Luca, F., Perfect Fibonacci and Lucas numbers, Rend. Circ. Mat. Palermo 49, 313-318, (2000).
7. Matveev, E.M., An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers II, Izv. Ross. Akad. Nauk Ser. Mat. 64, 125-180, (2000). Translation in Izv. Math. 64, 1217-1269, (2000).
8. Panda, G. K. and Davala, R. K., Perfect balancing numbers, Fibonacci Quart. 63(3), 261-264, (2015).
2. Bravo, J.J. and Luca, F., Perfect Pell and Pell–Lucas numbers, Stud. Sci. Math. Hung. 56(4), 381-387, (2019).
3. Bugeaud, Y., Mignotte, M. and Siksek, S., Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers, Ann. Math. (2) 163, 969-1018, (2006).
4. Dujella, A. and Petho, A., A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. 49, 291-306, (1988).
5. Faco, V. and Marques, D., Even perfect numbers among generalized Fibonacci sequences, Rend. Circ. Mat. Palermo 63, 363-370, (2014).
6. Luca, F., Perfect Fibonacci and Lucas numbers, Rend. Circ. Mat. Palermo 49, 313-318, (2000).
7. Matveev, E.M., An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers II, Izv. Ross. Akad. Nauk Ser. Mat. 64, 125-180, (2000). Translation in Izv. Math. 64, 1217-1269, (2000).
8. Panda, G. K. and Davala, R. K., Perfect balancing numbers, Fibonacci Quart. 63(3), 261-264, (2015).
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Publicado
2025-09-17
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Research Articles
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