Bounds for the size of sets with the property D(n)

Andrej Dujella
2004 Glasnik Matematicki - Serija III  
Let n be a nonzero integer and a 1 < a 2 < · · · < a m positive integers such that a i a j + n is a perfect square for all 1 ≤ i < j ≤ m. It is known that m ≤ 5 for n = 1. In this paper we prove that m ≤ 31 for |n| ≤ 400 and m < 15.476 log |n| for |n| > 400. 0 2000 Mathematics Subject Classification. 11D45, 11D09, 11N36.
doi:10.3336/gm.39.2.01 fatcat:6yhgwksm4fc6jo4y4veijeyk2e