MHB Proof & Structures: Showing n≤0 for Prime/Composite Number

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The discussion focuses on proving that for n ≤ 0, the expression n^2 - 14n + 40 results in a composite number. Participants are encouraged to factor the quadratic expression to analyze its properties. The key to determining when the expression is prime involves identifying integer values of n that yield one factor as ±1 and the other as a prime number. The conversation emphasizes the importance of understanding the relationship between the factors and their implications for primality. Overall, the thread seeks guidance on these mathematical proofs and explorations.
johnny009
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Hi There,

My apologies, there was an error...in a previous question, which I POSTED ....last week.

This question has now been withdrawn, & replaced with the following :

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a) Show that if n ≤ 0, then n^2 - 14n + 40 is a composite number.

b) Determine, with explanation, all integer values of 'n' for which ...n^2 -14n + 40 is prime

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any guidance on these issues.....will be fantastic!

Thanks a lot.

John
 
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johnny009 said:
a) show that if n ≤ 0, then n^2 - 14n + 40 is a composite number.

b) Determine, with explanation, all integer values of 'n' for which ...n^2 -14n + 40 is prime
Hint: Factorise the quadratic expression $n^2 - 14n + 40.$
 
If you have factorised $n^2 - 14n + 40$, then the only cases where this could represent a prime would be when one of the factors is $\pm1$ and the other factor is (plus or minus) a prime. Which values of $n$ give rise to those possibilities?
 
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