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Question

If P(n) : 2×42n+1+33n+1 is divisible by λ for all nϵN is true, then find the value of λ.


Solution

=2×42n+1+33n+1

=2×44n+2+33n+1

=44n+3+33n+1

Given above expression is divisible by λ for all nϵN

so lets check for n = 1

=128+81=209

for n = 2

=2048+2187=4235

Now its clearly evident that common factor for above numbers is 11 so λ=11.

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