Solution of Erdős problem # 443

Q: What does this research mean for the field?

The number of integers common to the sets {k(m−k):1≤k≤m2} and {l(n−l):1≤l≤n2} can be estimated, providing a solution to Erdős problem #443. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Stijn Cambie

doi:10.1080/00029890.2026.2694385

August 17, 2026American Mathematical MonthlyOpen Access

Solution of Erdős problem # 443

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Key Points

To resolve Erdős and Graham's problem #443 by estimating the number of common integers shared between two parameterized quadratic sets.
Analyzed the intersection of integer sets defined by the forms {k(m − k) : 1 ≤ k ≤ m/2} and {l(n − l) : 1 ≤ l ≤ n/2} for positive integers m and n.
Employed combinatorial and analytic number theory techniques to bound the number of coincident values.
Established quantitative bounds on the number of common elements between the two arithmetic sets.
Provided a complete theoretical resolution to the open problem posed by Erdős and Graham.

Implication

Mathematical analysis resolves Erdős-Graham problem 443 on shared values between integer sets, uncovering precise bounds on quadratic intersections.

Abstract

In [1, p.88], Erdős and Graham posed the following problem:Let m and n be positive integers and consider the two sets {k(m−k):1≤k≤m2} and {l(n−l):1≤l≤n2}.Can one estimate the number of integers com...

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Stijn Cambie (2026) studied this question.

synapsesocial.com/papers/6a85630603308d306e2d5f88 https://doi.org/10.1080/00029890.2026.2694385

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Solution of Erdős problem # 443

Key Points

Implication

Abstract

Discussion

Cite This Study

Solution of Erdős problem # 443

Key Points

Implication

Abstract

Discussion

Cite This Study

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