Processing math: 100%
World Scientific
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

On the size of Diophantine m-tuples in imaginary quadratic number rings

    https://doi.org/10.1142/S1664360719500206Cited by:9 (Source: Crossref)

    A Diophantine m-tuple is a set of m distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers. We study the same problem in the rings of integers of imaginary quadratic fields. By using a gap principle proven by Diophantine approximations, we show that m42. Our proof is relatively simple compared to the proofs of similar results in positive integers.

    Communicated by Efim Zelmanov

    AMSC: Primary: 11D09, Secondary: 11J68