Question

For how many positive integers n^3-8n^2+20n-13 is a prime

Answer 1

Answer:

for no positive integer n the expression yeilds a prime . one of its solutions is 1 ( not a prime ) and other two are irrationals [7+ (101)^1/2]/2 and [7-(101)^1/2]/2

Answer 2

Answer:

n^3- 8n^2+20n -13

= (n-1)(n^2 - 7n + 13 )

In order to make (n-1) prime it will either be +/-1 or (n^2 - 7n + 13 ) has to be +/-1

n-1 = +/-1

= n = 0 or 2

n^3- 8n^2+20n -13 = -13 or 3

(n^2 - 7n + 13 ) = +/-1

= n is 3 or 4.

For this we will get n^3- 8n^2+20n -13 = 2 or 3

We know that prime numbers are positive so the prime numbers will be 2,3 and 4.