NUMBER THEORY :
Tommy's conjecture : every positive integer is the sum of at most 8 pentatope numbers.
For those unfamiliar with " pentatope numbers " :
http://en.wikipedia.org/wiki/Pentatope_number
This is a natural generalization of Fermat's polygonal number theorem , Pollock's tetrahedral numbers conjecture and Pollock's octahedral numbers conjecture.
There exist stronger versions of this conjecture such that Fermat and Pollock's ideas are included.
But the pentatope numbers are key in how to generalize correctly.
Im not aware of an example that requires more then 7 pentatope numbers , then again I have not used a computer nor paper and I did not really search hard.
Or maybe I forgot about that example , it has been many years since I considered this for the first time.
regards
tommy1729
Tommy's conjecture : every positive integer is the sum of at most 8 pentatope numbers.
For those unfamiliar with " pentatope numbers " :
http://en.wikipedia.org/wiki/Pentatope_number
This is a natural generalization of Fermat's polygonal number theorem , Pollock's tetrahedral numbers conjecture and Pollock's octahedral numbers conjecture.
There exist stronger versions of this conjecture such that Fermat and Pollock's ideas are included.
But the pentatope numbers are key in how to generalize correctly.
Im not aware of an example that requires more then 7 pentatope numbers , then again I have not used a computer nor paper and I did not really search hard.
Or maybe I forgot about that example , it has been many years since I considered this for the first time.
regards
tommy1729