Concordant Form
A concordant form is an integer Triple 
where
with
and 
integers. Examples include  | |
 | |
 |
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 completewith 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.
- Recurrence Relation
- Recurrence Sequence
- Recurring Digital Invariant
- Recursion
- Recursive Function
- Recursive Monotone Stable Quadrature
- Red-Black Tree
- Red Net
- Reduced Amicable Pair
- Reduced Fraction
- Reduced Latitude
- Reducible Crossing
- Reducible Matrix
- Reducible Representation
- Reduction of Order
- Reduction Theorem
- Redundancy
- Reeb Foliation
- Reef Knot
- Re-Entrant Circuit
- Refinement
- Reflection
- Reflection Property
- Reflection Relation
- Reflexible