## Prime Representation

Let , , and denote Positive Integers satisfying

(i.e., both pairs are Relatively Prime), and suppose every Prime with is expressible if the form for some Integers and . Then every Prime such that and is expressible in the form for some Integers and (Halter-Koch 1993, Williams 1991).

 Prime Form Representation

References

Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 70-73, 1994.

Halter-Koch, F. A Theorem of Ramanujan Concerning Binary Quadratic Forms.'' J. Number. Theory 44, 209-213, 1993.

Williams, K. S. On an Assertion of Ramanujan Concerning Binary Quadratic Forms.'' J. Number Th. 38, 118-133, 1991.