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The authors posted some information on their discovery to Number Theory Listserver (and forwarded that message to me), but it seems that their post is not yet visible on listserv.nodak.edu/cgi-bin/wa.exe?A0=NMBRTHRY&TOC=&S=b
I received an announcement of the rank 17 curve in an email titled "j=0, rank 17" from Noam on Feb 23, 2016 (I was one of a dozen recipients). This document is dated Feb 18, 2016 math.harvard.edu/~elkies/many_pts_asu.pdf
The mentioned related conjecture that there does not exist a set of four positive integers with the property that the product of any two of them is 1 greater than a square was proved recently in the paper N. C. Bonciocat, M. Cipu, M. Mignotte, There is no Diophantine D(-1)-quadruple, J. London Math. Soc. 105 (2022), 63-99.
Concerning problem D29 (in the third edition), He, Togbe and Ziegler proved in 2019 that a Diophantine 5-tuple with property D(1) does not exist. Also, the bound for the size of a polynomial D(n)-m-tuple if n is a linear polynomial has been diminished from 26 to 12.
In fact, in Book V of Arithmetics written by Diophantus, in Exercise 9, we can find three rationals, and after scaling three integers with given property: 4843, 5358, 61206.
In paper A. Choudhry, Sextuples of integers whose sums in pairs are squares, Int. J. Number Theory 11 (2015), no. 2, 543–555. five examples of six distinct integers are given, but they also contain one negative number.
