COUNTING THE NUMBER OF SOLUTIONS TO THE ERDŐS–STRAUS EQUATION ON UNIT FRACTIONS

DOI10.1017/S1446788712000468zbMath1304.11018arXiv1107.1010MaRDI QIDQ2852274

Christian Elsholtz, Terence C. Tao

Publication date: 8 October 2013

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.1010

zbMATH Keywords

Average value of arithmetical functionErdős-Strauss ConjectureSolution of a Diophantine equation by polynomials.Upper and lower bounds of arithmetical function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Diophantine equations in many variables (11D72) Rational numbers as sums of fractions (11D68) Rate of growth of arithmetic functions (11N56)

Related Items (17)

On \(\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{2}\) and some of its generalizations ⋮ Ternary Egyptian fractions with prime denominator ⋮ A note on the Erd\H{o}-Straus Conjecture ⋮ Explicit upper bound for the average number of divisors of irreducible quadratic polynomials ⋮ On the average number of divisors of reducible quadratic polynomials ⋮ Partial Proof Without Words: Shaping Some Cases of the Erdős–Straus Conjecture ⋮ Revisiting the average number of divisors of a quadratic polynomial ⋮ Factorization length distribution for affine semigroups. I: Numerical semigroups with three generators ⋮ Brauer–Manin obstruction for Erdős–Straus surfaces ⋮ On the number of divisors of the least common multiples of shifted prime powers ⋮ On Egyptian fractions of length 3 ⋮ A note on the Erdős-Straus conjecture ⋮ The number of solutions of the Erdős-Straus Equation and sums ofkunit fractions ⋮ Error term of the mean value theorem for binary Egyptian fractions ⋮ On ternary Egyptian fractions with prime denominator ⋮ Sums of four and more unit fractions and approximate parametrizations ⋮ Explicit upper bound for an average number of divisors of quadratic polynomials

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