## Distinct powers

### Problem 29

Published on Friday, 25th October 2002, 06:00 pm; Solved by 46051

Consider all integer combinations of ab for 2 a 5 and 2 b 5:

> 22=4, 23=8, 24=16, 25=32
> 32=9, 33=27, 34=81, 35=243
> 42=16, 43=64, 44=256, 45=1024
> 52=25, 53=125, 54=625, 55=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for 2 a 100 and 2 b 100?