Proof of Lucas

Set $r := n$ , $q := k$

(( ... , k _{1} , k _{0} ) _{p} ( ... , n _{1} , n _{0} ) _{p}) \equiv (( ... , k _{2} , k _{1} ) _{p} ( ... , n _{2} , n _{1} ) _{p}) (k _{0} n _{0}) \equiv ... \equiv \prod (k _{i} n _{i})

So when is $(k n)$ odd?

(k n) = \prod (k n) m o d 2

Criterion for you parity of $(k n)$
$(k n)$ is odd ⇐> binaryform of $n$
dominates binaryform of $k$ .

Quartz 4