On The Diophantine Equation Ba + 67p = y2

Sudhanshu  Aggarwal; Lalit Mohan Upadhyaya

doi:10.48165/

Authors

Sudhanshu Aggarwal Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur-273402, Uttar Pradesh, India
Lalit Mohan Upadhyaya Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun-248179, Uttarakhand, India

DOI:

https://doi.org/10.48165/

Keywords:

Diophantine Equation, Catalan Conjecture, Solution, Integers

Abstract

In this paper, authors have examined the Diophantine equation 8a + 67f3 = y , where a, {3, y are non-negative integers, for non-negative integer solutions. Authors used Catalan’s conjecture for this purpose. Results of the present paper show that the Diophantine equation 8a + 67f3 = y , where a, {3, y are non-negative integers, has a unique solution in non-negative integers and this solution is given by (a, {3, y) = (1, 0, 3).

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