Positive Integers , , , and which satisfy

(1) |

(2) |

A set of Pythagorean quadruples is given by

(3) | |||

(4) | |||

(5) | |||

(6) |

where , , and are Integers,

(7) |

(8) |

(9) | |||

(10) | |||

(11) | |||

(12) |

(Carmichael 1915).

**References**

Carmichael, R. D. *Diophantine Analysis.* New York: Wiley, 1915.

Mordell, L. J. *Diophantine Equations.* London: Academic Press, 1969.

Oliverio, P. ``Self-Generating Pythagorean Quadruples and -tuples.'' *Fib. Quart.* **34**, 98-101, 1996.

© 1996-9

1999-05-26