Let be the prime-counting function and be a non-constant rational function. Can we have for infinitely many values of ?
A 'rational function' can be written as...
(1)
... where and are polynomial in x of degree n and m so that we can write...
(2)
... or equivalently...
(3)
At the end of nineteenth century it has been demonstrated that is...
(4)
... or equivalently...
(5)
Combining (3) and (5) we find that is...
(6)
... so that the situation described by NCA is impossible...
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