[psyang]

Originally Posted by psyang

New problem.

Does there exist any two distinct integers a and b such that 2^a is just a rearrangement of the digits of 2^b?

A rearrangement of the digits is when the same digits are re-ordered to make a new number: 12345 is a rearrangement of 45321. It is not a rearrangement of 4532 or 453212 or 4532.1 for example.

If yes, provide an example. If no, show why not.

No bites? This one is definitely a bit more in the number theory category.

Hint

Spoiler!

If 2^a and 2^b are rearrangements of their digits, they must have the same number of digits which limits how far apart a and b can be.

It also means they must have the same digits, which may make the mod operator useful.