FT16: Summary of Modular Formulas for F(kn+m) and L(kn+m)

• F(kn + m) ≡ (−1)^nk/2 F (m) (mod F(n)),
  for k even.

• F(kn + m) ≡ (−1)^n(k−1)/2 F (m) F(n−1) (mod F(n)),
  for k odd.

• L(kn + m) ≡ (−1)^nk/2 L (m) (mod F(n)),
  for k even.

• L(kn + m) ≡ (−1)^n(k−1)/2 L (m) F(n−1) (mod F(n)),
  for k odd.

• F(kn + m) ≡ (−1)^(n+1)k/2 F (m) (mod L(n)),
  for k even.

• 5 F(kn+m) ≡ (−1)^{(n+1)(k−1)/2} L(m) L(n−1) (mod L(n)),
  for k odd.

• L(kn + m) ≡ (−1)^(n+1)k/2 L(m) (mod L(n)),
  for k even.

• L(kn+m) ≡ (−1)^{(n+1)(k−1)/2} F(m) L(n−1) (mod L(n)),
  for k odd.