janosfazekas91 wrote:
If n is a prime number, which of the following could be true?
A. n^n=n
B. n^2/4= is even
C. (n)(n^n) = is negative
D. n^2+n^3= n^5
E. n^n/4 = 1^(n-1)
right away, we can eliminate C - prime number multiplied by another prime number raised to itself - can never be negative.
n^n=n only when n=1. thus, it can't be. A is out.
B - never true. if n=2, then it's odd. if n is any other prime number, then the result is a non-integer.
D - try with the lowest possible prime numbers: 2^2+2^3 = 4+8=12. can't be expressed as n^5. with n=3 the same..the more we try, the more we realize it's impossible.
E however, works fine. if n=2, then 2^2/4 = 1. and 1^(2-1) = 1. which is true.
so E it is possible.