Find the base of the numeration system in which 135/21 has a zero remainder.

neurolover25
Feb 10, 2018

#1**+1 **

If your 135/21 are ALREADY converted to the desired base, then:

135_7 mod 21_7 =0 remainder.

This does make sense, since 135_7 = 75_10, and 21_7 = 15_10. So, 75/15 =5 with no remainder.

Guest Feb 10, 2018

edited by
Guest
Feb 10, 2018

edited by Guest Feb 10, 2018

edited by Guest Feb 10, 2018

#2**+1 **

This was answered by Melody a few days ago...I believe that she found the answer to be base 7 as follows:

[ 1b^2 + 3b + 5 ] / [ 2b + 1] and when b = 7 we have that

[ 7^2 + 3*7 + 5 ] / [ 2*7 + 1 ] =

[ 49 + 21 + 5 ] / [ 15 ]

[ 70 + 5 ] / [ 15] =

[ 75] / [ 15] =

5

CPhill
Feb 10, 2018