A280945 List of primitive triples (x, y, z) of positive integers for which xy - z, yz - x, and zx - y are powers of 2.

2, 2, 2, 2, 2, 3, 2, 6, 11, 3, 5, 7

Offset

1,1

Comments

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).

See the proof in the link.

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).

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

Links

Table of n, a(n) for n=1..12.

56th International Mathematical Olympiad, Problem N5, 70-72.

Art of Problem Solving, 2015 IMO Problems.

Victor Pambuccian, A problem in Pythagorean Arithmetic, arXiv:1510.01645 [math.LO], 2015.

Index to sequences related to Olympiads.

Example

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.

Crossrefs

Sequence in context: A165054 A067743 A029230 * A349949 A196067 A251141

Adjacent sequences: A280942 A280943 A280944 * A280946 A280947 A280948

Keyword

nonn,fini,full,tabf

Author

Michel Lagneau, Jan 11 2017

Status

approved