OFFSET
2,1
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 10.13
FORMULA
Row n = (a, b, c, d) = (2n^2 + 4n + 1, 4n^2 + 2n, 4n^2 + 2n, 6n^2 + 4n + 1).
EXAMPLE
Table begins:
n=2: 17, 20, 20, 33;
n=3: 31, 42, 42, 67;
n=4: 49, 72, 72, 113;
n=5: 71, 110, 110, 171;
n=6: 97, 156, 156, 241;
MATHEMATICA
cuaternas={}; Do[cuaternas=Join[cuaternas, {2n^2+4n+1, 4n^2+2n, 4n^2+2n, 6n^2+4n+1}], {n, 2, 35}]; cuaternas
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Miguel-Ángel Pérez García-Ortega, Apr 22 2024
STATUS
approved