OFFSET
1,1
COMMENTS
This type of equation is used in the Fermat-Catalan conjecture, the ABC conjecture, etc., of course, with additional restrictions and conditions.
LINKS
Anatoly E. Voevudko, Table of n, a(n) for n = 1..7253
Anatoly E. Voevudko, Description of all powers in b265731
Anatoly E. Voevudko, Description of all powers in b245713
Anatoly E. Voevudko, Description of all powers in b261782
Wikipedia, abc conjecture
Wikipedia, Fermat-Catalan conjecture
EXAMPLE
8 = 2^3 = 2^2 + 2^2; 9 = 3^2 = 1^3 + 2^3; 16 = 4^2 = 2^3 + 2^3; etc.
PROG
(PARI) A265731(lim, bflag=0)={my(Lcz=List(1), Lb=List(), czn, lczn, lbn, lim2=logint(lim, 2), lim3);
for(z=2, lim2, lim3=sqrtnint(lim, z); for(C=2, lim3, listput(Lcz, C^z)));
Lcz=Set(Lcz); lczn = #Lcz; if(lczn==0, return(-1));
for(i=1, lczn, for(j=i, lczn, czn=Lcz[i]+Lcz[j]; if(czn>lim, break);
if(setsearch(Lcz, czn), listput(Lb, czn)))); listsort(Lb, 1); lbn=#Lb;
if(bflag, for(i=1, lbn, print(i , " ", Lb[i]))); if(!bflag, return(Vec(Lb))); }
\\ Anatoly E. Voevudko, Nov 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Anatoly E. Voevudko, Dec 14 2015
STATUS
approved