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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Glasnik Matematicki Serja III.
( Vol. 39 NO.2 / (2004))
Bounds for the size of sets with the property
Andrej Dujella,
Pages. 199-205
Abstract Let ${it n}$ be a nonzero integer and ${it a}_1 < {it a}_2 < cdots < {it a}_{it m}$ positive integers such that ${it a}_{it i}{it a}_{it j}+{it n}$ is a perfect square for all $1 leq {it i} < {it j} leq {it m}$. It is known that ${it m} leq 5$ for ${it n}=1$. In this paper we prove that ${it m} leq 31$ for $|{it n}| leq 400$ and ${it m} < 15.476 log|{it n}|$ for |{it n}| > 400$.
Contents 1.Introduction
2.Three lemmas
3.Proof of proposition 1.1
4.Proof of proposition 1.2
Key words Diophantine ${\it m}$-tuples, property ${\sl D}({\it n})$, large sieve
Mathmatical Subject Classification 11D45, 11D09, 11N36