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To illustrate, the solution + = has bases with a common factor of 3, the solution + = has bases with a common factor of 7, and + = + has bases with a common factor of 2. Indeed the equation has infinitely many solutions where the bases share a common factor, including generalizations of the above three examples, respectively
The Beal conjecture, also known as the Mauldin conjecture [162] and the Tijdeman-Zagier conjecture, [163] [164] [165] states that there are no solutions to the generalized Fermat equation in positive integers a, b, c, m, n, k with a, b, and c being pairwise coprime and all of m, n, k being greater than 2.
Beal's conjecture: number theory: Andrew Beal: 142 Beilinson conjecture: number theory: Alexander Beilinson: 461 Berry–Tabor conjecture: geodesic flow: Michael Berry and Michael Tabor: 239 Big-line-big-clique conjecture: discrete geometry: Birch and Swinnerton-Dyer conjecture: number theory: Bryan John Birch and Peter Swinnerton-Dyer: 2830 ...
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"Any solutions to the Beal conjecture will necessarily involve three terms all of which are ...." It is unfortunate to say a "solution" is to "the Beal conjecture". Each "solution" referred to here is a point (A,B,C) of the locus {(A,B,C) ∈ ℕ 3 | A x + B y = C z}. It is entirely correct to say that (A,B,C) is a solution to the equation A x ...
Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics includes the aesthetics and culture of mathematics, peculiar or amusing stories and coincidences about mathematics, and the personal lives of mathematicians.
A number theorist, Beal is also known for the Beal conjecture, [5] a mathematical generalization of Fermat's Last Theorem. He has funded a $1 million standing prize for its proof or disproof. [ 6 ] His banks sponsor two annual science and technology fairs affiliated with the International Science & Engineering Fair. [ 7 ]
A 2-spot game of Sprouts. The game ends when the first player is unable to draw a connecting line between the only two free points, marked in green. The game is played by two players, [2] starting with a few spots drawn on a sheet of paper. Players take turns, where each turn consists of drawing a line between two spots (or from a spot to ...