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proof by existence??
can anybody help me on this problem ...
i can show by Disproof by counterexample
for all integers n>= 1
suppose n^2  7n + 49 is prime
try n =1 then it is equal to 43, still prime
if n = 2 then 39, composite
Disproof:
n^2  7n + 49 is not a prime for some integer n>=1.
but for this problem i can not seem to express how it should be done.. :(
thanks a lot so much.

Re: proof by existence??
Seriously, are you even trying to do these problems yourself? Do you not see that "7n+ 49= 7(n+ 7)" is divisible by 7 for all n? What does that mean for $\displaystyle n^2$"?
No, that is not a "disproof by counter example" because the problem does NOT assert that "$\displaystyle n^2 7n+ 49$ is divisible by 7 for all n". The problem is to show that there exists at least one such n. The fact that there exist n for which it is NOT true is irrelevant.
You have posted a large number of widely diverse problems in which you seem to have no idea what they are about or even what they are asking. What is going on here?

Re: proof by existence??
HallsofIvy sorry i was not expecting your reply... i never posted it for you actually... you might not know the answer either :p
if you have nothing to say good and your reply is just a an insult ... well that is not the reason why im here... im here for the answer or guide or help ... not that... if you have nothing good to message/tell/reply .. better not say it or what. you are not the only helper who could answer or help me. i would never say all these things if never had done that to me also.
thanks and God Bless.
Be good at all times
according to
Confucianism
"Do not do to others what you would not like yourself. Then there will be no resentment against you, either in the family or in the state."
THANKS AND SORRY TOO..