More on Diophantine Equations
Sanjay Tahiliani
Dr. Sanjay Tahiliani*, Lecturer, N.K. Bagrodias, Rohini, Sec 9, New Delhi-110085, India.
Manuscript received on August 31, 2020. | Revised Manuscript received on February 26, 2021. | Manuscript published on February 28, 2021. | PP: 26-27 | Volume-5 Issue-6, February 2021. | Retrieval Number: 100.1/ijmh.L10810841220 | DOI: 10.35940/ijmh.L1081.025621
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© The Authors. Published By: 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 paper, we will find the solutions of many Diophantine equations. Some are of the form 2(3 x )+ 5(7y ) +11=z2 for non negative x, y and z. we also investigate solutions of the Diophantine equation 2(x+3) +11(3y ) ─ 1= z2 for non negative x, y and z and finally, we study the Diophantine equations (k!×k)n = (n!×n)k and ( 𝒌!÷𝒌 ) 𝒏 = ( 𝒏÷𝒏 ) 𝒌 where k and n are positive integers. We show that the first one holds if and only if k=n and the second one holds if and only if k=n or (k,n) =(1,2),(2,1).We also investigate Diophantine equation u! + v! = uv and u! ─ v! = uv .
Keywords: Exponential Diophantine equations.