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

Abstract

In this paper, authors have studied the Diophantine equation 𝑟³ − 15𝑟² +71𝑟−104 = 5^𝑠, 𝑟,𝑠 ∈ 𝑍0, where 𝑍0 represents the set of non-negative integers, for determining the ordered pairs (𝑟,𝑠) ∈ 𝑍0 ×𝑍0 that satisfy the equation 𝑟³ − 15𝑟² +71𝑟 −104 = 5𝑠. For this task, authors have considered the well known modular arithmetic technique. It was shown by the results that the ordered pairs (𝑟,𝑠) = (3,0),(5,0),(7,0) ∈ 𝑍0 × 𝑍0 are the only solutions of the Diophantine equation 𝑟³ − 15𝑟² +71𝑟 −104 = 5^𝑠.