:Help...........for how many positive integers n is n^3 -8n^2+20n-13 a prime number??

- King

:Help...........for how many positive integers n is n^3 -8n^2+20n-13 a prime number??

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- anonymous

factorize it

- King

how watever i get is not a prime number

- King

why?

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## More answers

- King

oh

- King

but then ii have to plug in millions of values

- anonymous

what u want to calculate

- anonymous

(n^3 -8n^2+20n-13) a prime number

- anonymous

or n is a prime number

- King

for n i will have to put millions of values to find how may n positive integers satisfy n^3 -8n^2+20n-13 to be a prime number

- anonymous

ok

- King

so,what to do??

- King

anything i can do to narrow down the possobilities

- King

no answer given....

- anonymous

ok see for 2 it is prime number

- anonymous

wait i took wrong concept

- anonymous

\[(x-1) \times [(x-7)x + 13]\]

- anonymous

where x is n

- King

ok

- anonymous

now see the first term is (x-1).
and other than 2 no other even number is a prime number right

- anonymous

i got the answer

- King

no n does not have to be a prime number n^3 -8n^2+20n-13 has to be a prime number

- anonymous

yeah i know
(x−1)×[(x−7)x+13]
it has to be prime

- King

yup so x can be anything greater or equal to 2

- anonymous

first term is (x-1) and two is the only even prime number.

- anonymous

but if u will subtract 1 from any other prime number the resultant will be divisible by 2

- anonymous

getting my point or not

- King

x can be 4

- anonymous

yeah u r right

- anonymous

it means that for any odd integer other than 3 u will not get a prime number

- King

yeah

- anonymous

Superb sheggy!

- anonymous

also the number cannot be graeter than 7

- King

oh yeah

- anonymous

thanks fool bhai

- anonymous

so u are having a limited space to work out that is from 1 to 7

- King

yes sheg u got it so answer is n=2,3,4

- King

no actually 2 to 7

- anonymous

hahahaa right 2 to 7

- anonymous

but for 7 it will be 0

- King

wait why cant it be greater than 7?

- anonymous

try any number u will get the answer

- anonymous

odd numbers cannot be included ok thats true

- anonymous

as i had told u any odd number subtracted by one will result in even number so it will be divisible by 2.........do u accept it or not

- King

is 323 a prime number?

- King

yeah i acept

- King

its not div by 17

- anonymous

323 is divisible by 17

- anonymous

so 323 is not a prime number

- King

4387
?

- anonymous

what u have put x = ??

- King

n=20

- King

1443?

- King

gtg shall come bak in 15 min

- anonymous

for n = 20 it should be equal to 5187

- King

oh yeah 1443?

- King

no

- anonymous

20^3 - 8*20^2 + 20*20 -13
=8000 - 3200 + 400 -13
= 8400 - 3213
= 5187

- King

gtg cum bak in 15 mins

- anonymous

dear i had told u for no value greater than 7 it would fit

- anonymous

and both 1443 and 5187 is divisible by 3

- King

i am bak
so what to do now?

- anonymous

for no value greater than 7 that too even number it will not be a prime number

- anonymous

http://www.wolframalpha.com/input/?i=x^3-8x^2%2B20x-13+where+x+%3D+20
visit this website and plug in different value of x u will get the answer

- anonymous

king u there

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