Prove that 11n+2 + 122n+1 is divisible by 133 for all n belongs to N .
for n =1 we get
3059/133 = 23
hence it is true for n =1
let us assume that this expression is true for n = k
is divisible by 133
for n = k+1
=
=
which is divisible by 1331+1728 = 3059 which is divisible by 133
hence our assumption is correct and is divisible by 133