344
 

344-28k with k an integer

344-28*10=2^6
344-28*11=6^2
344-28*12=2^3

Given two positive integers m and n,
Consider m-k*n with k positive and m-k*n positive.
Are there other numbers m, n, k such that for consecutive k's m-k*n is a power?
In the example for consecutive k=10,11,12

344-28*10 is a power
344-28*11 is a power
344-28*12 is a power