smc

Question

The base-nine representation of the number N is 27,006,000,052_nine. What is the remainder when N is divided by 5?

Accepted Answer

Recall that 9-15. We expand N by the definition of bases: align* N&=27,006,000,052_9 &= 29^10 + 79^9 + 69^6 + 59 + 2 & 2(-1)^10 + 7(-1)^9 + 6(-1)^6 + 2 &&5 & 2-7+6+2 &&5 & 3 &&5. align*