344

enzocreti · 2020-02-01, 09:58

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

2020-02-01, 09:58	#1
enzocreti Mar 2018 2·5·53 Posts	344 344-28k with k an integer 344-2810=2^6 344-2811=6^2 344-2812=2^3 Given two positive integers m and n, Consider m-kn with k positive and m-kn positive. Are there other numbers m, n, k such that for consecutive k's m-kn is a power? In the example for consecutive k=10,11,12 344-2810 is a power 344-2811 is a power 344-28*12 is a power