A given year p (expressed in YYYY format) is defined as "Ambiguous" if there exists at least one positive integral solution of the equation x^2 + x + y^2 + 3y = p. Otherwise, the said year (p) is a "Definite" year.

For example, 1890 A.D. was an "Ambiguous" year, since (x,y)=(34,25) corresponds to a positive integral solution of x^2 + x + y^2 + 3y = 1890.

Determine, whether 2006 A.D. is an Ambiguous Year or a Definite Year.

I am definite that 2006 is a Definite Year. No positive integral solutions are available.

1890 also is Ambiguous with (X,Y) = (26,33). Does this make it Double Ambiguous?

Posted by Leming on 2006-02-27 10:42:51