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Each of X, Y and Z is a distinct positive integer such that
X, Y and Z are in arithmetic sequence, and
X, Y and Z+2016 are in geometric sequence.

Find the four smallest values of X+Y+Z.

(No Solution Yet, 1 Comments) Submitted on 2016-04-29 by K Sengupta   
Difficulty: 2 of 5 Bonus: Ambiguous And Definite Years (in Numbers) Rating: 3.00
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.

(Solution Posted, 4 Comments) Submitted on 2006-02-27 by K Sengupta   
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