Originally Posted by twisted_logic89
Originally Posted by twisted_logic89
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
aah I am lost again, just when i thought I had it.
can anyone point me in the right direction? I am so close I can taste it.... and smell it a bit too....
2p is even when n is odd and odd when n is even...right?
Originally Posted by twisted_logic89
I'm not sure that I know the answer to this question.
We know that 2p is the product of n - 1 and n + 1, for natural numbers n.
These two factors will always be two consecutive odd integers OR two consecutive even integers, dependent upon a specific n.
What happens when you multiply two even numbers? What happens when you multiply two odd numbers?
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
Originally Posted by twisted_logic89
YES!
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
YES! ... was this an enthusiastic "you're on the right track" yes or an exasperated why-are-you-stating-the-obvious yes?
even * even = even
odd * odd = odd
Look at the equationOriginally Posted by twisted_logic89
[tex]p \, = \, \frac{1}{2}\cdot (n+1)\cdot (n-1)[/tex]
p has been factorized - is it possible with a prime number?
“... mathematics is only the art of saying the same thing in different words” - B. Russell
Originally Posted by twisted_logic89
The former.
Since you now realize that the product of n - 1 and n + 1 is even for some values of n, can any of those values of n lead to a product which is twice some prime number?
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
prime numbers cant be factorized right?
can any values of n lead to a product which is twice some prime number? since twice some prime number will be even, then only odd n values would work right?
Originally Posted by twisted_logic89
2p = EVEN
2p = (n - 1) * (n + 1)
Therefore, (n - 1) * (n + 1) must also be EVEN.
This is enough information to eliminate half of the natural numbers from being part of any solution.
Please tell me which natural numbers cannot possibly be part of any solution.
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
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