A concordant form is an integer Triple where

with and integers. Examples include
Dickson (1962) states that C. H. Brooks and S. Watson found in *The Ladies' and Gentlemen's Diary* (1857) that
and can be simultaneously squares for only for 1, 7, 10, 11, 17, 20, 22, 23, 24, 27,
30, 31, 34, 41, 42, 45, 49, 50, 52, 57, 58, 59, 60, 61, 68, 71, 72, 74, 76, 77, 79, 82, 85, 86, 90, 92, 93, 94, 97, 99,
and 100 (which evidently omits 47, 53, and 83 from above). The list of concordant primes less than 1000 is now complete
with the possible exception of the 16 primes 103, 131, 191, 223, 271, 311, 431, 439, 443, 593, 607, 641, 743, 821,
929, and 971 (Brown).

*See also *Congruum

**References**

Brown, K. S. ``Concordant Forms.''
http://www.seanet.com/~ksbrown/kmath286.htm.

Dickson, L. E. *History of the Theory of Numbers, Vol. 1: Divisibility and Primality.*
New York: Chelsea, p. 475, 1952.

© 1996-9 *Eric W. Weisstein *

1999-05-26