Question

For what least positive value of of n the expression $3^{4n}-4^{3n}$ is exactly divisible ?

Answer 1

(34n−43n)=(34)n−(43)n=81n−64n(34n−43n)=(34)n−(43)n=81n−64n
So by (i) above this expression is divisible by
(81-64) is by 17.