OFFSET
1,2
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, Cuaternas pitagóricas
FORMULA
Row n = (a, b, c, d) = (1, 2*n, 2*n^2, 2*n^2 + 1).
EXAMPLE
Table begins:
n=1: 1, 2, 2, 3;
n=2: 1, 4, 8, 9;
n=3: 1, 6, 18, 19;
n=4: 1, 8, 32, 33;
n=5: 1, 10, 50, 51;
MATHEMATICA
cuaternas={}; Do[cuaternas=Join[cuaternas, {1, 2n, 2n^2, 2n^2+1}], {n, 1, 35}]; cuaternas
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Miguel-Ángel Pérez García-Ortega, Mar 01 2024
STATUS
approved