All right!... it is self evident that is an integer that we can indicate with k. Because and and is...
(1)
... we have to suppose that is . Now we proceed 'step by step' to verify with increasing value of k starting from 0...
(2)
and because , is solution of (1)...
(3)
and because , is also solution of (1)...
For k>1 there are no more solution , so that the (1) has two solutions... like a 'standard' second order equation ...
Kind regards