On Infinite Number of Solutions for one type of Non-Linear Diophantine Equations
V Yegnanarayanan1, Veena Narayanan2, R Srikanth3
1V. Yegnanarayanan, PhD, Department of Mathematics, Annamalai University, Tamil Nadu, India.
2Veena Narayanan, Research student, Department of Mathematics, Calicut University, Kerala, India.
3R Srikanth, Professor, Department of Mathematics (Mathematics, Number theory), Bharathidasan University, Tiruchirappalli, Tamil Nadu, India.
Manuscript received on October 13, 2019. | Revised Manuscript received on 24 October, 2019. | Manuscript published on November 10, 2019. | PP: 1665-1669 | Volume-9 Issue-1, November 2019. | Retrieval Number: A4706119119/2019©BEIESP | DOI: 10.35940/ijitee.A4706.119119
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this article, we prove that the non-linear Diophantine equation 𝑦 = 2𝑥1𝑥2 …𝑥𝑘 + 1; 𝑘 ≥ 2, 𝑥𝑖 ∈ 𝑃 − {2}, 𝑥𝑖′𝑠 are distinct and P is the set of all prime numbers has an infinite number of solutions using the notion of a periodic sequence. Then we also obtained certain results concerning Euler Mullin sequence.
Keywords: Prime Number, Diophantine Equation, Periodic Sequence, Periodic function.
Scope of the Article: Algorithm Engineering