Pandiagonal Type-p Franklin Squares

TL;DR

This paper introduces a new class of magic squares called type-p Franklin squares, generalizing classical Franklin squares to prime powers and constructing them for orders that are prime powers.

Contribution

It defines and constructs type-p Franklin squares for prime-power orders, extending the classical Franklin squares to a broader mathematical setting.

Findings

Defined type-p Franklin squares for prime p.

Constructed these squares for prime-power orders.

Generalized Franklin squares beyond the classical case.

Abstract

For prime $p$ we define magic squares of order $kp^3$, called type-$p$ Franklin squares, whose properties specialize to those of classical Franklin squares in the case $p=2$. We construct type-$p$ Franklin squares in prime-power orders.