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Solving a Mathematical Mystery: Schinzel's Conjecture

ISEF · 2018 Mathematics

Sathyanarayanan, Sacheth · National Public School

Overview

In 1948, Paul Erdos and Ernst G Straus formulated the Erdos-Straus Conjecture, which states that for any natural number n, the equation 4/n=1/x + 1/y + 1/z is solvable in positive integers x, y and z. This is an open problem in mathematics and has no solution as of yet. Mordell has proved it for all numbers except those primes that are congruent 1, 121, 169, 289, 361, or 529 modulo 840. Andrzej Schinzel later generalized this conjecture, stating that for any positive integer m, there exists a natural number N such that, for all integers n greater than or equal to N, there exists a solution in positive integers to m/n=1/x + 1/y + 1/z. This project aims to prove Schinzel’s conjecture, especially the case m=6.

Awards (1)

  • Mu Alpha Theta, National High School and Two-Year College Mathematics Honor Society: First Award of $ 1,500 $1,500

Competition history

  • ISEF 2018 Mathematics · Entry MATH049 Affiliated fair in Delhi, India

Resources

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Source: Regeneron International Science and Engineering Fair

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