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        riddles >> hard >> Century, Prime Year And Sum Of Squares
        
(Message started by: K Sengupta on Dec 2^nd, 2005, 11:08pm)

Title: Century, Prime Year And Sum Of Squares
Post by K Sengupta on Dec 2^nd, 2005, 11:08pm

Considering that N is a positive whole number, it is observed that a year (Y) belonging to a decade in the Nth Century is such that none of the years in the said decade is divisible by 13 and the year under reference constitutes the only prime number in the said decade.
Determine the total number of Y's corresponding to N in the range 1<=N<=8901 which satisfies conditions of the problem such that each Y is expressible as the sum of squares of two distinct positive integers. ( For example, it can be verified that there is only one year corresponding to N=33, satisfying all the conditions in terms of the first paragraph, which is given by Y=3299. However, 3299 CANNOT be expressed as sum of squares of two positive integers.)