On the Diophantine Equation

In this paper, authors have examined the Diophantine equation 𝑟3 − 4𝑟2 +3𝑟+1= 5𝑠, 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 − 4𝑟2 + 3𝑟 + 1 = 5𝑠. 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 (𝑟,𝑠) = (0,0),(1,0),(3,0) ∈ 𝑍0 × 𝑍0 are the only solutions of the Diophantine equation 𝑟3 − 4𝑟2 + 3𝑟 + 1 = 5𝑠.