perplexus.info :: Sequences : Brazilian numbers

Brazilian numbers (Posted on 2017-07-15)

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.)

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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