/PartitionExponentialNumber

Exploring a special way to partition positive integers, where we express each integer as a sum of powers of n.

Primary LanguagePythonMIT LicenseMIT

Consider the following question:
'Can all even numbers be uniquely expressed as a sum of powers of two, without using each powers of two more than once.'
E.g.
18=16*1+8*0+4*0+2*1 (therefore the answer is yes for 18)
We can generalize the question to:
"For a chosen number n, can all positive integers be uniquely expressed as a sum of g*n^k's, where 0<=g<n, k>1, and all g, n, k are integers."
e.g. 
17=9*1 + 3*2 + 1*2.
I suspect the answer is yes after thinking about modular arithmatic for a bit, so I went to verify it with the python script partition_test.py.