The unit digit in the sum of (124)^372 + (124)373 is

Sure, let's solve this step by step:

1. First, we need to find the unit digit of (124)^372 and (124)^373 separately.

2. The unit digit of a number raised to a power depends only on the unit digit of the base number. So, we only need to consider the unit digit of 124, which is 4.

3. The cycle of unit digits for 4 raised to successive powers is 4, 6, 4, 6, and so on. This cycle repeats every 2 powers.

4. Therefore, the unit digit of (124)^372 is 6 because 372 is an even number and the unit digit of (124)^373 is 4 because 373 is an odd number.

5. Now, we add these two unit digits: 6 + 4 = 10.

6. The unit digit of 10 is 0.

So, the unit digit in the sum of (124)^372 + (124)^373 is 0.