Consider the expression, 2.(42n+1)+33n+1=P(n) P(n)=8(42n)+3(33n) For n =1, P(n=1)=128+81 =209 Above is divisible by 19 and 11. Similarly, P(n=2)=2048+2187 =4235 Above is divisible by 11 but not by 19.1So, the given expression is divisible by, k=11,n∈N