chetan2u wrote:
ak1802 wrote:
Here's my explanation, I tried to keep it simple:
The question is essentially asking us if x is a prime, or can be factored into a single prime.
St (1): tells us that 2 is not a factor of x. We know this because if 16(x) has one less prime factor than x, that "one less prime factor" is 2. However, we still do not know whether x is prime or not. N.S.
2^8 =16, for those who wonder how that association is made.
For example:
x can equal 15 which satisfies the condition in st(1), but doesn't solve the problem.
x can also equal 3 which satisfies the condition in st(1) and DOES solve the problem.
St (2) tells us that 2(x)^16 only has two primes. This means that x can be factored into a single prime number OR x has 2 and another prime as its prime factors.
St(1) and St (2) tell us that, working with St(2) first; 2(x)^16 only has two primes. St(1) tells us that 2 is not a factor of x. Therefore x must be a prime number.
C.
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hi,
it is not necessary x will be a prime number ... it can be a square of a prime number... only surety is that it has only one prime number as factor
Yes, you're correct. I stated above that the question is asking if X can either be prime, or factored into a single prime.
[edit] didn't notice the red text on my phone. You're right, error on my part in St(1) and St(2). X must be an integer, that can be factored into a
single prime number, other than 2.
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