6=m^p-n^q?

[ZAKIRS]

Dear All, thank you very much for the instructive discn.
 
as to 6  - this is my another typo: 6 should be in the list 
(and 10 removed hence subject).
 
OK, and what the number theory says now:
can 6 be represented as difference of two full powers (not powerful numbers)
or not? 
Only imagine  these lots of fullpowers and why not differ by 6? zak
 
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