• Melvyn Knight's Problem

    Updated: 2023-01-31 15:46:33
    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 Melvyn Knight's Problem Melvyn Knight once asked 1 for which integers is there an integer triple so that For example , 11 has two such representations : and Solutions for this problem can be found using elliptic curves 1 This Demonstration shows a sample solution for all solvable values from to When one solution exists , there are an infinite number of . solutions Contributed by : Ed Pegg Jr THINGS TO TRY Slider Zoom Gamepad Controls Automatic Animation SNAPSHOTS DETAILS The original problem 1 may be rewritten as and further rewritten as Solving for leads to a complicated expression equivalent to the elliptic : curve

  • An Algebraic Identity for Powers 0, 1, 2, 3 and 5

    Updated: 2023-01-31 15:46:33
    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 An Algebraic Identity for Powers 0, 1, 2, 3 and 5 Let be three arbitrary numbers and set Then for In this Demonstration , and are . integers For , example 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 Simultaneous Diophantine Equations for Powers 1, 2, 4 and 6 Wolfram Demonstrations Project A Four-Power Diophantine Equation

  • Algebraic Identity with Twelve Variables

    Updated: 2023-01-31 15:46:33
    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 Algebraic Identity with Twelve Variables Let be five arbitrary complex numbers . Set and Then for In this Demonstration , and are . integers For , example 13 5 169 5 221 5 39 5 299 5 117 5 21 5 203 5 189 5 7 5 301 5 119 5 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 Simultaneous Diophantine Equations for Powers 1, 2, 4 and 6

  • Algebraic Identity with Squares and Seventh Powers

    Updated: 2023-01-31 15:46:33
    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 Algebraic Identity with Squares and Seventh Powers Let be two arbitrary complex numbers . Then set The result is In this Demonstration , and are . integers For , example 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 Simultaneous Diophantine Equations for Powers 1, 2, 4 and 6 Wolfram Demonstrations Project A Four-Power Diophantine

  • Algebraic Identity for Sum of Seven Terms with Exponents 1, 2, 4, 6 and 8

    Updated: 2023-01-31 15:46:33
    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 Algebraic Identity for Sum of Seven Terms with Exponents 1, 2, 4, 6 and 8 Let be two arbitrary numbers and set Then for In this Demonstration , and are . integers For , example 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 Simultaneous Diophantine Equations for Powers 1, 2, 4 and 6 Wolfram Demonstrations Project A Four-Power

  • A Two-Power Algebraic Identity

    Updated: 2023-01-31 15:46:33
    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 A Two-Power Algebraic Identity Let be four arbitrary complex numbers and set Then we have and In this Demonstration , and are . integers For : example 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 Simultaneous Diophantine Equations for Powers 1, 2, 4 and 6 Wolfram Demonstrations Project A Four-Power Diophantine Equation Wolfram

  • A Three-Term Algebraic Identity with Squares or Quartics

    Updated: 2023-01-31 15:46:33
    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 A Three-Term Algebraic Identity with Squares or Quartics Let be two arbitrary . numbers Set Then for In this Demonstration , and are . integers For , example 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 Simultaneous Diophantine Equations for Powers 1, 2, 4 and 6 Wolfram Demonstrations Project A Four-Power Diophantine Equation

  • A Six-Variable Algebraic Identity with Squares and Cubes

    Updated: 2023-01-31 15:46:33
    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 A Six-Variable Algebraic Identity with Squares and Cubes Given three rational numbers and define the following six : quantities Then for we have In this Demonstration , and are . integers For : example 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 Simultaneous Diophantine Equations for Powers 1, 2, 4 and 6 Wolfram Demonstrations

  • A Four-Term Algebraic Identity for Powers 1, 2, 3 and 5

    Updated: 2023-01-31 15:46:33
    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 A Four-Term Algebraic Identity for Powers 1, 2, 3 and 5 Let be three arbitrary numbers and set Then for In this Demonstration , and are . integers For , example 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 Simultaneous Diophantine Equations for Powers 1, 2, 4 and 6 Wolfram Demonstrations Project A Four-Power Diophantine Equation

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