Discussion

What is the remainder when \(9^{19} + 6\) is divided by 8?

Answer: D

We can solve this in two parts. First, find the remainder of \(9^{19} \div 8\). Since \(9 = 8+1\), the expression is \((8+1)^{19} \div 8\). The remainder will be \(1^{19}\), which is 1. Second, find the remainder of \(6 \div 8\), which is 6. The final remainder is the sum of these remainders, divided by 8 if necessary. Remainder = \((1 + 6) \div 8 = 7 \div 8\). The remainder is 7.