(n^3-12n^2+8n-93)/(11+2n-n^2)=
10-n+(n+203)/(n^2-2n-11)
so for this to be an integer we need
n+203>=n^2-2n-11
which for integer n is only true when
-13<=n<=16
from this we get that the only integer solutions are
(n,p):
(-3,63)
(-2,-55)
(1,-8)
(4,-63)
(5,57)
From these, the only one where p is prime is when n=5 which gives p=57.
Thus the only possible prime value for p is 57 and thus the sum is 57.
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Posted by Daniel
on 2019-07-22 09:14:38 |
No Subject
