10=m^p-n^q?
Don Reble
djr at nk.ca
Mon Oct 7 22:12:43 CEST 2002
> i've just speculated that somel integers can't be represented as
> "difference of two full powers >=2"
One can immediately represent the odd numbers and the multiples of four,
as differences of two squares. Of the rest,
2 = 3^3 - 5^2
6
10 = 13^3 - 3^7 (Thanks, Neil)
14
18 = 3^3 - 3^2
22 = 7^2 - 3^3
26 = 3^3 - 1^2
30 = 83^2 - 19^3
34
38 = 37^2 - 11^3
42
46 = 17^2 - 3^5
50
54 = 3^4 - 3^3
...
I haven't yet found reps for 6, 14, 34, 42, 50, 58, 62, 66, 70, 78, ...
Zak, do you have one for 6?
--
Don Reble djr at nk.ca
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