On the Diophantine Equation ð’“👠− ðŸ’ð’“ðŸ + ðŸ‘ð’“ + ðŸ = ðŸ“s
Sudhanshu Aggarwal
2025Journal of Advanced Research in Applied Mathematics and Statistics11 citationsDOIOpen Access PDF
Abstract
In this paper, authors have examined the Diophantine equation ð‘Ÿ3 − 4ð‘Ÿ2 +3ð‘Ÿ+1= 5ð‘ , ð‘Ÿ,ð‘ ∈ ð‘0, where ð‘0 represents the set of non negative integers, for determining the ordered pairs (ð‘Ÿ,ð‘ ) ∈ ð‘0 × ð‘0 that satisfy the equation ð‘Ÿ3 − 4ð‘Ÿ2 + 3ð‘Ÿ + 1 = 5ð‘ . For this purpose, authors have considered the well known modular arithmetic technique. It was shown by the results of this paper that the ordered pairs (ð‘Ÿ,ð‘ ) = (0,0),(1,0),(3,0) ∈ ð‘0 × ð‘0 are the only solutions of the Diophantine equation ð‘Ÿ3 − 4ð‘Ÿ2 + 3ð‘Ÿ + 1 = 5ð‘ .
Topics & Concepts
Diophantine equationLegendre's equationMathematicsDiophantine setThue equationSet (abstract data type)Diophantine geometryDiscrete mathematicsInteger (computer science)Pure mathematicsModular equationCornacchia's algorithmAlgebra over a fieldSet theoryCongruence (geometry)Modular designInterval (graph theory)ArithmeticAdvanced Mathematical Theories and ApplicationsAnalytic Number Theory ResearchAlgebraic Geometry and Number Theory