Y by
Let
be a positive integer and
a prime number. Consider the sequence
defined by
Let
be the smallest prime such that some term of the sequence is divisible by
. Determine all pairs
for which
.



![\[
a_n = (p - 2)^n + p^n - m, \quad \text{for } n \geq 1.
\]](http://latex.artofproblemsolving.com/5/9/e/59e2074875b2d41f1e2ac272d06e65f3ebab85ff.png)




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