Permutation polynomials over finite fields form a central theme in modern algebraic research, intertwining group theory, number theory and combinatorial design. A finite field is a set of elements ...

Before being mortally wounded in a duel at age 20, Évariste Galois discovered the hidden structure of polynomial equations. By studying the relationships between their solutions — rather than the ...

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs. When you deposit a quarter and turn the crank on a gumball machine, the ...

Diophantine equations, named after the ancient mathematician Diophantus of Alexandria, are polynomial equations whose solutions are sought in integers or rational numbers. From the simplest linear and ...