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: A4706119119/2019Β©BEIESP | DOI: 10.35940/ijitee.A4706.119119
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Abstract: In this article, we prove that the non-linear Diophantine equation 𝑦 = 2π‘₯1π‘₯2 …π‘₯π‘˜ + 1; π‘˜ β‰₯ 2, π‘₯𝑖 ∈ 𝑃 βˆ’ {2}, π‘₯𝑖′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