Primes of the Form 4m + 1

Year 2017, Volume: 7, 16 - 20, 19.12.2017

Öznur Öztunç Kaymak

https://izlik.org/JA29MR52NN

Abstract

In this paper a new equation related to the sums of the squares of the first n k-Fibonacci numbers has
been found. From this equation, the problem of existing infinitely many primes exist p such that p =1 (mod4) of
elemantary number theory is obtained.

Keywords

k-Fibonacci number , Prime numbers

References

• Bolat, C., Köse, H., On the Properties of k-Fibonacci Numbers, Int. J. Contemp. Math. Sciences, 5, (2010), 1097-1105.
• Hoggat, V., Long, C., Divisibilty Properties of Generalized Fibonacci Polynomials, Fibonacci Quart. 12, 10M05, (1974), 113-120.
• Falcon, S., On the k-Lucas numbers, Int. J. Contemp. Math. Sci. 6, (2011), 21-24.
• Kalman, D., Mena, R., The Fibonacci Numbers-Exposed, Math. Mag. 76, no. 3, (2003), 167-181.
• Kilic, E., Sums of the squares of terms of sequence fUng, Proc. Indian Acad. Sci. (Math. Sci.) 118, (2008), 27-41.
• Koshy, T., Fibonacci and Lucas Numbers with Applications, Wiley, 2001.
• Ozgur, N. Y., Kaymak, O. O., On determination of k-Fibonacci and k-Lucas numbers, Math. Sci. Appl. E-notes, 3(2015), 20-26.
• Robbins, N., On Fibonacci Numbers and Primes of the form 4k + 1, The Fibonacci Quarterly 32, (1994), 15-16.