16th Putnam 1956

Given any positive integer n, show that we can find a positive integer m such that mn uses all ten digits when written in the usual base 10.

Solution

Thanks to Dror Speiser for this neat solution

Let n have d digits. Take N = 12345678900 ... 0, ending in d+1 digits. One of N+1, N+2, ... , N+n must be a multiple of n and its first 10 digits are all different.

16th Putnam 1956

© John Scholes
jscholes@kalva.demon.co.uk
4 Dec 1999
Last corrected/updated 6 Aug 03