It is a well known fact that any positive integer can be represented by a sum of at most 9 positive cubes, not necessarily distinct.
Dickson showed that the only integers requiring nine cubes are X
Find the values of X and Y , without referring to OEIS .
BTW, both numbers are below 300.
I didn't come up with this problem, but I still think it's a good one.
There are 4 positive integers in order from least to greatest, such that the first three make an aritmetic sequence, and the last three make a geometric sequence. If the difference between the largest and smallest term is 30, what are the terms?