"Driver, is this bus on time?"

Two other formulas from part 16 contain terms with the factor F ( m ), and so can be treated similarly to the previous post. These are: ...

Let's look at the first two congruences from the previous section : F ( kn + m ) ≡ (−1) nk /2 F ( m ) (mod F ( n )), for k ev...

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...

In this section, we look at the remaining four formulas from part 13, reducing them modulo L ( n ): 5 k /2 F ( kn + m ) = ∑ 0 ≤ j ≤ ...

Next we'll look at the formulas from part 13, but taken modulo F ( n ) or L ( n ). First, though, let's mention a couple of simple ...

The previous two sections covered a variety of formulas for F ( kn + m ) and L ( kn + m ); we summarize them here. Formulas for the Fibonac...

Let's follow the method of the last section, but using the formula ( L ( kn −1) + φ L ( kn ))/√ 5 = ( L ( n −1) + φ L ( n )) k /√ 5 k...