I'd like to find a number that's the difference of fourth powers in three ways or more. I.e.: $$k=a^4-b^4=c^4-d^4=e^4-f^4$$ Is this possible?
There seem to be plenty of examples of differences of fourth powers in two ways. The smallest: $$300783360=133^4−59^4=158^4−134^4$$
I've checked numbers $a,b$ up to ~$10,000$ with a python script with no results.