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Brazilian numbers (Posted on 2017-07-15) Difficulty: 3 of 5
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?

See The Solution Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips re: Part 1 Solution and more Comment 4 of 4 |
(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
  Posted by Ady TZIDON on 2017-07-28 11:52:17

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