For all but one positive integer triplet (a, b, c) with a ≼ b ≼ c and b ≼ 6, we decide whether there are algebraic numbers α, β and ϒ of degrees a, b and c, respectively, such that α + β + γ = 0. The ...

THE general outlines and the methods employed by the author will be familiar to readers who have seen the first volume. He has made a study of standard works and papers by Bachmann, Hensel, Hubert, ...

Mathematicians have found a framework for the celebrated Rogers-Ramanujan identities and their arithmetic properties, solving another long-standing mystery stemming from the work of Indian math genius ...

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...

This is a preview. Log in through your library . Abstract David R. Richman proved that for n ≥ k ≥ 2 every integral n × n matrix is a sum of seven k-th powers. In this paper, in light of a question ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

Courtney Gibbons is affiliated with the Association for Women in Mathematics and the American Mathematical Society. You might remember learning about the quadratic formula to figure out the solutions ...