Q4 of 66 Page 12

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

for n=1,

2×42×1+1 + 33×1+1=2×43+34


= 2×64+81


= 128+81


= 209


For n=2,


2×42×2+1 + 33×2+1 = 2×45+37


= 2×1024+2187


= 2048+2187


= 4235


Now, the H.C.F of 209 and 4235 is 11.


Hence, λ=11.


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