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%I #18 Mar 17 2021 08:01:19
%S 2,2,2,2,2,3,2,6,11,3,5,7
%N List of primitive triples (x, y, z) of positive integers for which xy - z, yz - x, and zx - y are powers of 2.
%C There are sixteen such triples, namely (2, 2, 2), the three permutations of (2, 2, 3), and the six permutations of each of (2, 6, 11) and (3, 5, 7).
%C See the proof in the link.
%C The sixteen triples are (2, 2, 2), (2, 2, 3), (2, 3, 2), (3, 2, 2), (2, 6, 11), (2, 11, 6), (6, 2, 11), (6, 11, 2), (11, 2, 6), (11, 6, 2), (3, 5, 7), (3, 7, 5), (5, 3, 7), (5, 7, 3), (7, 3, 5) and (7, 5, 3).
%C This sequence is relative to the 2nd problem, proposed by Serbia, during the 56th International Mathematical Olympiad in 2015 at Chiang Mai, Thailand (see links). - _Bernard Schott_, Mar 17 2021
%H 56th International Mathematical Olympiad, <a href="https://imo-official.org/problems/IMO2015SL.pdf">Problem N5, 70-72</a>.
%H Art of Problem Solving, <a href="https://artofproblemsolving.com/wiki/index.php/2015_IMO_Problems">2015 IMO Problems</a>.
%H Victor Pambuccian, <a href="https://arxiv.org/abs/1510.01645">A problem in Pythagorean Arithmetic</a>, arXiv:1510.01645 [math.LO], 2015.
%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%e The 3rd primitive triple (x, y, z) = (2, 6, 11) is in the sequence because xy - z = 1, yz - x = 2^6 and zx - y = 2^4.
%K nonn,fini,full,tabf
%O 1,1
%A _Michel Lagneau_, Jan 11 2017