I believe there are some mistakes in the problem statement, can anyone confirm this?

1.

For every natural number

, we have that for some

,

is equivalent to

modulo

(i.e.

divides

).

Shouldn't this be: For every natural number

, we have that for some

,

is equivalent to

modulo

2.

one can prove that this sequence does not contain any primes by using the following easy-to-prove identity, which holds for any Fibonacci-like sequence:

.

And this one:

?