@zabeer agreed bro. But go through this thread. There are 5-6 more wrong questions. And I have few friends who actually believed the solution. Really appreciate the collection and greatful for it, but many people would follow solutions as it is. Anger is on the part that a friend who showed this actually did same mistake in mock saying that he learnt the solution from here.
Hope you understand. No offense.
f(7)^2 - f(6)^2 = 517
(f(7) + f(6)) (f(7) - f(6)) = 517 = 11 x 47
As 11 and 47 cannot be further factorized and f(7) or f(6) should be natural numbers, we can say
f(7) + f(6) = 47 (Largest prime factor should come from their sum)
f(7) - f(6) = 11 (smallest prime factor should come from their difference)
solving, f(7) = 29 and f(6) = 18
f(10) = f(8) + f(9)
= f(7) + f(6) + f(7) + f(8)
= f(7) + f(6) + f(7) + f(7) + f(6)
3f(7) + 2f(6) = 3 x 29 + 2 x 18 = 123.
