A number of 50 digits has all its digits equal to 1 except the 26th digit. If the number is divisible by 13, then find the digit in the 26th place.
my solution is 9
the digit is the solution of the following equation:
(10^50 1)/9 + (x1)10^24 = 13k (K natural)
using Charlie's remarks regarding modulo 13 and the power series of 10,
10^50 1 + 9(x1)10^24 = 0 (mod 13)
91+12y=0 (mod 13), where y = x1
y=8, thus x=9
solution x=9

Posted by luminita
on 20031231 11:27:06 