A function V(a, b) is defined for positive integers a, b

Hello M7MBA.

This is a little long question. Here is how I'd solve it.

V(a, a) = a,
V(a, b) = V(b, a),
V(a, a+b) = (1 + a/b) V(a, b).

Using the second property we have $$V(66,14)=V\left(14,66\right)$$ Now, using the third property many times we get: $$V\left(14,66\right)=V\left(14,\ 14+52\right)=\left(1+\frac{14}{52}\right)V\left(14,52\right)=\frac{33}{26}V\left(14,52\right).$$ $$V\left(14,52\right)=V\left(14,\ 14+38\right)=\frac{26}{19}V\left(14,38\right).$$ $$V\left(14,38\right)=V\left(14,\ 14+24\right)=\frac{19}{12}V\left(14,24\right)$$ $$V\left(14,24\right)=V\left(14,14+10\right)=\frac{12}{5}V\left(14,10\right).$$ $$V\left(14,10\right)=V\left(10,14\right)=V\left(10,\ 10+4\right)=\frac{7}{2}V\left(10,4\right).$$ $$V\left(10,4\right)=V\left(4,10\right)=V\left(4,4+6\right)=\frac{5}{3}V\left(4,6\right).$$ $$V\left(4,6\right)=V\left(4,4+2\right)=3V\left(4,2\right).$$ $$V\left(4,2\right)=V\left(2,4\right)=V\left(2,2+2\right)=2V\left(2,2\right)=2\cdot2=4.$$ Now, we have to replace all the results as follows: $$V\left(14,66\right)=\frac{33}{26}\cdot\frac{26}{19}\cdot\frac{19}{12}\cdot\frac{12}{5}\cdot\frac{7}{2}\cdot\frac{5}{3}\cdot3\cdot4=\frac{33\cdot7\cdot4}{2}=33\cdot7\cdot2=462.$$ Since the answer is none of A, B, C or D, then the answer is [spoiler]E=none of the foregoing[/spoiler].

I hope it is clear enough.