+0

# Numerical bases?

0
479
4
+77

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

Feb 10, 2018

#1
+1

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.

Feb 10, 2018
edited by Guest  Feb 10, 2018
edited by Guest  Feb 10, 2018
#2
+101090
+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

Feb 10, 2018
edited by CPhill  Feb 11, 2018
#3
0

Wow  !!  I didn't see Melody's answer, but that is very interesting way of doing it !!. So, you would arrive at the answer by trial and error? Or, is there a sure way of surmising the answer?

Feb 10, 2018
#4
+101090
0

She used trial and error....but..with the presence of the "5"  she knew that the base had to  be  6 or greater.......so...it didn't take her long to get to 7....LOL!!!!

Feb 11, 2018