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Topic: A Digital Transference Problem (Read 319 times) |
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K Sengupta
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A Digital Transference Problem
« on: Nov 28th, 2005, 12:25am » |
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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.
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