Problem: When the number 21000 is divided by 13, the remainder in the division is
Answer Choices:
A. 1
B. 2
C. 3
D. 7
E. 11
Solution:
The remainder in the division of 213 by 13 is 1 because that of 26=64 is$ -1$ . Hence 21000=2996×24=(212)83×16 leaves a remainder of 183×3=3 when divided by 13 .
or
Using congruences, 24≡−1mod13. Hence 21000≡2996×24≡(−1)164×16≡1×3=3mod13.