15^145 mod 26 = 15
If you do the actual division, this is what you should get:
15^145 / 26 =1312983338 7719885766 1024601110 7556846410 9960169490 7167019486 7931722744 5648476512 7652340511 7917837585 4355823111 0988664260 7746973976 4592875193 1985691324 0913015145 5218975360.576 923 076 923 .
If you multiply the fraction 0.576 923 076 923 x 26 = 15 - which is the remainder.
I attempted it this way. We know that 15^145 = 15^5(29). I then took 15^5 mod 26, or 19. Then, I took 19^29 mod 26, which gave me 15.