Suppose, $a,b\ge 2$ are integers. Then $$N=a^b$$ is a perfect power. Assuming that $a$ is not divisible by $10$, are there infinite many such perfect powers consisting of at most $2$ distinct decimal digits ?
The first few perfect powers with the desired property are :
? for(j=1,10^7,if(Mod(j,10)<>0,if(ispower(j)>0,if(length(Set(digits(j)))<=2,prin
t1(j," ")))))
4 8 9 16 25 27 32 36 49 64 81 121 144 225 343 441 484 676 1331 1444 7744 7776 11
881 29929 44944 55225 69696 9696996
?
Additionally, I found the square $$6661661161$$
Are there more examples, and if yes, are there infinite many examples ?