OFFSET
2,2
COMMENTS
A Pythagorean quadruple is a quadruple (a,b,c,d) of positive integers such that a^2 + b^2 + c^2 = d^2 with a <= b <= c. Its inradius is (a+b+c-d)/2, which is a positive integer.
REFERENCES
Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
LINKS
Miguel-Ángel Pérez García-Ortega, Teorema 10.12
FORMULA
Row n = (a, b, c, d) = (2n^2 - 1, 4n^2 + 6n + 2, 4n^2 + 6n + 2, 6n^2 + 8n + 3).
EXAMPLE
Table begins:
n=1: 1, 12, 12, 17;
n=2: 7, 30, 30, 43;
n=3: 17, 56, 56, 81;
n=4: 31, 90, 90, 131;
n=5: 49, 132, 132, 193;
MATHEMATICA
cuaternas={}; Do[cuaternas=Join[cuaternas, {2n^2-1, 4n^2+6n+2, 4n^2+6n+2, 6n^2+8n+3}], {n, 1, 35}]; cuaternas
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Miguel-Ángel Pérez García-Ortega, Apr 22 2024
STATUS
approved