Perfect Difference Set
A Set of Residues 
(mod 
) such that everyNonzero Residue can be uniquely expressed in the form 
. Examples include
(mod 7) and 
(mod 13). A Necessary condition for a difference set to exist is that be of the form 
. A Sufficient condition is that 
be a Prime Power. Perfect sets can be usedin the construction of Perfect Rulers.
References
Guy, R. K. ``Modular Difference Sets and Error Correcting Codes.'' §C10 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 118-121, 1994.
- Free Semigroup
- Freeth's Nephroid
- Free Variable
- Freiman's Constant
- French Curve
- Frenet Formulas
- Frequency Curve
- Fresnel Integrals
- Fresnel's Elasticity Surface
- Fresnel's Wave Surface
- Frey Curve
- Frey Elliptic Curve
- Friday the Thirteenth
- Friend
- Friendly Giant Group
- Friendly Pair
- Frieze Pattern
- Frobenius-König Theorem
- Frobenius Map
- Frobenius Method
- Frobenius-Peron Equation
- Frobenius Pseudoprime
- Frobenius Theorem
- Frobenius Triangle Identities
- Frontier