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        riddles >> hard >>  A Digital  Transference Problem
        
(Message started by: K Sengupta on Nov 28^th, 2005, 12:25am)

Title: A Digital Transference Problem
Post by K Sengupta on Nov 28^th, 2005, 12:25am

Considering a K digit integer N ( where the last digit of N is non-zero) the number G constituted by deleting the last P digits of N and shifting a permutation of these P digits ( the definition of the said permutation being inclusive of the original last P Digits of N) to the beginning of N.
IF:
(i) G is divisible by N such that G is not equal to N,
determine the total number of pairs (G,N) where 2<=P<=6 ,8<=K<=15 and Max(G,N)<10^15

(ii) If, in addition, the sum of the digits in N is a perfect M-th power with M being a positive whole number grater than 1, determine the total number
of distinct Quadruplets ( P,K, G,N) where 2<=P<=6 ,8<=K<=15 and Max(G,N)<10^15.

(iii) Determine the minimum possible magnitude of
the pair (G,N) separately for each pair (P,K) where
2<=P<=6 ,8<=K<=15 and Max(G,N)<10^15.