Oh! Prime Number
Number Theory
Level
4
How many are those positive integers such that is prime?
2
3
1
4
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1 solution
n²-14n+24 =n²-2.7.n+7²-25 =(n-7)²-5² =(n-7+5)(n-7-5) =(n-2)(n-12) So, if n=1 then (1-2)(1-12)=(-1)(-11)=11 which is prime number. If n=13 also,then (13-2)(13-12)=11.1=11 which is prime number It is a matter that, in this case the way to find the value of n is [(n-2)(n-12)] must not have more than one factor. That’s mean, if we want to solve this problem, we have to make either (n-2) or (n-12) equal 1 or (-1) . So, the answer is 2.