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        riddles >> medium >> Base P Integers
        
(Message started by: K_Sengupta on Nov 27^th, 2005, 10:16pm)

Title: Base P Integers
Post by K_Sengupta on Nov 27^th, 2005, 10:16pm

A two digit Base-P integer N is such that the sum of the digits of a Base-P number K ( in base-P notation) is divisible by P(2P-3) where the magnitude of K is equivalent to (P^N - N) in Base-10 (decimal) notation.
(i) For which P satisfying 5<=P<=25 do solutions exist?
(ii) If in addition, N is expressible as the sum of two squares and the sum of digits of N is a prime number, would any solution to the problem , corresponding to the range of P in terms of Clause (i), still exist?