Discussion

What is the unit digit of \(37^{37} - 23^{23}\)?

Answer: A

We find the unit digit of each term. For \(37^{37}\), we need the unit digit of \(7^{37}\). Cycle for 7 is (7,9,3,1), length 4. \(37\div 4\) rem 1. So unit digit is 7. For \(23^{23}\), we need the unit digit of \(3^{23}\). Cycle for 3 is (3,9,7,1), length 4. \(23\div 4\) rem 3. So unit digit is 7. The unit digit of the difference is the unit digit of \(7-7=0\). The result is 0.