Find the last 2 digit of 31^26

To find the last two digits of 31^26, we can use the concept of cyclicity.

1. First, we need to find the cycle of the last two digits of powers of 31.

2. The last two digits of 31^1 is 31, 31^2 is 961 (so 61), 31^3 is 29791 (so 91), 31^4 is 923521 (so 21), 31^5 is 28629151 (so 51), 31^6 is 887503681 (so 81), 31^7 is 27512614111 (so 11), 31^8 is 852891037441 (so 41), 31^9 is 26439622160671 (so 71), 31^10 is 819628286980801 (so 01), and 31^11 is 25397369317840631 (so 31).

3. We can see that the cycle repeats every 10 powers (31, 61, 91, 21, 51, 81, 11, 41, 71, 01, 31).

4. Now, we need to find the remainder when 26 is divided by 10, which is 6.

5. So, the last two digits of 31^26 will be the same as the last two digits of 31^6, which is 81.

So, the last two digits of 31^26 are 81.