Minimising a Ratio

Let N = 3⁴⁵ + 4⁵⁶ = F1 * F2 (F1 < F2) Find F1 and F2 proper divisors of N that minimise ^{(F2 - F1)} / _N. Answer format: F1,F2 where F1 and F2 is entered using the following condensed representation: Leading 10 digits[number of digits not shown]trailing 10 digits For example, 2¹²⁷ in this representation would be shown as 1701411834[19]5884105728