(A) Jason likes primes and he was excited by Wacko Calculator
. He has a calculator that allows him to add, subtract, multiply and divide in positive integer bases up to 36. Jason chose two base N positive integers X and Y, with N being a positive integer between 10 and 36 inclusively, where X and Y are relatively prime having the proviso that sod(X) is prime. Thereafter, he divided X by Y to obtain: .01234567890123456789.....
Determine the values of N for which this is possible.
(B) Keeping all the other conditions in (A) unaltered but disregarding the proviso that sod(X) is a prime number – Jason noted that there is precisely one value of N between 10 and 36 inclusively such that X is a prime number.
What is the value of N and what are the corresponding values of X and Y?
: sod(x) denotes the sum of digits of x.
(In reply to Question (partial spoiler?)
by Dej Mar)
Since the dividend and divisor (that is X and Y) are both base N positive integers- in conformity with the provisions inclusive of the problem text, 0.01234567890123456789... is a base-N fraction (and not necessarily a decimal fraction.)
Edited on August 29, 2010, 4:24 am