- #1
charmedbeauty
- 271
- 0
uhh! help with this proof """" then x is prime""".
For a positive integer x≥2.
"if x is not divisible by any positive integer n satisfying 2≤n≤√x then x is a prime number"
a) show that the above statement is true .
b) Is the statement still true if the condition on n is replaced by 2≤n<√x ??
Well firstly I really have problems with proofs in general, but
x≥4
so x can be [4,5,6,7,...∞)
so by definition of prime number x--> x/x and x/1
but I really don't know how to approach this
I know its true because n= [2,3,4,5...∞)
and so the only numbers not possibly divisible by n are primes, Since n can be any positive integer ≥2, and Since x≠1.
But how do I put it in mathematical terms??
HELP!
Homework Statement
For a positive integer x≥2.
"if x is not divisible by any positive integer n satisfying 2≤n≤√x then x is a prime number"
a) show that the above statement is true .
b) Is the statement still true if the condition on n is replaced by 2≤n<√x ??
Homework Equations
The Attempt at a Solution
Well firstly I really have problems with proofs in general, but
x≥4
so x can be [4,5,6,7,...∞)
so by definition of prime number x--> x/x and x/1
but I really don't know how to approach this
I know its true because n= [2,3,4,5...∞)
and so the only numbers not possibly divisible by n are primes, Since n can be any positive integer ≥2, and Since x≠1.
But how do I put it in mathematical terms??
HELP!