Definition: "Brazilian" numbers ("les nombres brĂ©siliens" 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)

You say:

....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.

You mean:

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**