Arto Adili

ON THE SEQUENCES $\{a_n\}$ AND $\{b_n\}$ DEFINED BY $p^n=a_n^2 + b_n^2$, WHERE $p$ IS A PRIME OF THE FORM $p \equiv 1 (\text{mod} 4)$

Let $p \equiv 1$ (mod 4) be a prime number, and consider its representation as a sum of two squares, $$p=a^2 + b^2,$$ for some integers $a$ and $b$. In this paper, we study the sequences $\{a_n\}$ and $\{b_n\}$ defined by the relation $$p^n=a_n^2 + b_n^2,$$ arising from powers of the Gaussian integer $a+bi$. In Sectio...