Group Theory

Number Magic with Squares

Updated: 2023-03-31 17:36:34

12,000+ Interactive Demonstrations Powered by Notebook Technology TOPICS LATEST ABOUT AUTHORING AREA PARTICIPATE Your browser does not support JavaScript or it may be disabled Number Magic with Squares Let be two arbitrary numbers and set Then for Contributed by : Minh Trinh Xuan THINGS TO TRY Slider Zoom Gamepad Controls Automatic Animation SNAPSHOTS RELATED LINKS abc Conjecture Wolfram Demonstrations Project Coincidences in Powers of Integers Wolfram Demonstrations Project Diophantine Equation Wolfram MathWorld Seven Points with Integral Distances Wolfram Demonstrations Project Algebraic Identity for Powers 1, 2, 4 and 6 Wolfram Demonstrations Project A Four-Power Algebraic Identity Wolfram Demonstrations Project PERMANENT CITATION Minh Trinh Xuan Number Magic with Squares http :

Fundamental Unit

Updated: 2023-03-31 17:36:34

12,000+ Interactive Demonstrations Powered by Notebook Technology TOPICS LATEST ABOUT AUTHORING AREA PARTICIPATE Your browser does not support JavaScript or it may be disabled Fundamental Unit For a squarefree integer the number is a fundamental unit if Basically , there are no fractions in either the number or its reciprocal . For example , the fundamental unit of is The reciprocal of the fundamental unit is For squarefree integers mod 4 the value is a fundamental unit if In these cases , is . allowed Thus , the fundamental unit is either or Except for the golden ratio , one of the continued fraction convergents of is Also , equals one of the values There are no smaller integers and that give that value for the given Contributed by : Ed Pegg Jr THINGS TO TRY Slider Zoom Gamepad Controls

A Host–Kra F^omega_2-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the U^6(F^n_2) norm; The structure of totally disconnected Host–Kra–Ziegler factors, and the inverse theorem for the U^k Gowers uniformity norms on finite abelian groups of bounded torsion

Updated: 2023-03-10 15:45:21

Asgar Jamneshan, Or Shalom, and myself have just uploaded to the arXiv our preprints “A Host–Kra -system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the norm” and “The structure of totally disconnected Host–Kra–Ziegler factors, and the inverse theorem for the Gowers uniformity norms on finite […]