Can you proof the following?
For each integer #n in N#
#5n^3+7n^5-=0# (mod 12)
For each integer
2 Answers
See below.
Explanation:
Given
we have that a typical polynomial such that
then making
we have
so choosing
or
where
then as
See explanation...
Explanation:
For any integer
If
If
Hence for any integer
Hence
Then modulo
So:
#0 -= 7n^3(n-1)(n+1) = 7n^3(n^2-1) = 7n^5-7n^3 -= 5n^3+7n^5#