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.
