Definition: "Brazilian" numbers ("les nombres brésiliens" in French)are numbers n such that exists a natural number k with 1<k< (n-1) such that
the representation of n in base k has all equal digits.
1.Prove that all even numbers above 6 are Brazilian numbers.
2. How many odd Brazilian numbers are there below 100?
(In reply to Part 1 Solution and more
by Brian Smith)
....This can be generalized to all composite numbers of at least 6. Factor the number into f*g with f>1 and g>2. Then the composite can be written as ff in base g-1.
1....at least 8
2. ... Factorize the number into f*g with g>f and f>1. Then the composite can be written as ff in base g-1.
so: 100=11 base 99 = 22 base 49 = 44 base 24 etc.
You can edit your post to eliminate errors.
Edited on July 29, 2017, 7:09 am