On the Diophantine Equation 𝒓𝟑 − 𝟏𝟓𝒓𝟐 + 𝟕𝟏𝒓 − 𝟏𝟎𝟒 = 𝟓𝒔

Abstract

In this paper, authors have studied the Diophantine equation 𑟳 − 15𑟲 +71ð‘Ÿâˆ’104 = 5^ð‘ , ð‘Ÿ,𑠠∈ 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 𑟳 − 15𑟲 +71𑟠−104 = 5ð‘ . For this task, authors have considered the well known modular arithmetic technique. It was shown by the results that the ordered pairs (ð‘Ÿ,ð‘ ) = (3,0),(5,0),(7,0) ∈ ð‘0 × ð‘0 are the only solutions of the Diophantine equation 𑟳 − 15𑟲 +71𑟠−104 = 5^ð‘ .