King
:Help...........for how many positive integers n is n^3 8n^2+20n13 a prime number??



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sheg
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factorize it

King
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how watever i get is not a prime number

King
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why?

King
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oh

King
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but then ii have to plug in millions of values

sheg
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what u want to calculate

sheg
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(n^3 8n^2+20n13) a prime number

sheg
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or n is a prime number

King
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for n i will have to put millions of values to find how may n positive integers satisfy n^3 8n^2+20n13 to be a prime number

sheg
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ok

King
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so,what to do??

King
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anything i can do to narrow down the possobilities

King
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no answer given....

sheg
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ok see for 2 it is prime number

sheg
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wait i took wrong concept

sheg
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\[(x1) \times [(x7)x + 13]\]

sheg
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where x is n

King
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ok

sheg
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now see the first term is (x1).
and other than 2 no other even number is a prime number right

sheg
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i got the answer

King
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no n does not have to be a prime number n^3 8n^2+20n13 has to be a prime number

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

King
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yup so x can be anything greater or equal to 2

sheg
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first term is (x1) and two is the only even prime number.

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

sheg
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getting my point or not

King
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x can be 4

sheg
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yeah u r right

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

King
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yeah

FoolForMath
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Superb sheggy!

sheg
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also the number cannot be graeter than 7

King
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oh yeah

sheg
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thanks fool bhai

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

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

King
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no actually 2 to 7

sheg
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hahahaa right 2 to 7

sheg
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but for 7 it will be 0

King
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wait why cant it be greater than 7?

sheg
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try any number u will get the answer

sheg
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odd numbers cannot be included ok thats true

sheg
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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
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is 323 a prime number?

King
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yeah i acept

King
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its not div by 17

sheg
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323 is divisible by 17

sheg
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so 323 is not a prime number

King
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4387
?

sheg
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what u have put x = ??

King
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n=20

King
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1443?

King
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gtg shall come bak in 15 min

sheg
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for n = 20 it should be equal to 5187

King
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oh yeah 1443?

King
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no

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

King
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gtg cum bak in 15 mins

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

sheg
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and both 1443 and 5187 is divisible by 3

King
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i am bak
so what to do now?

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


sheg
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king u there