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.