prove or disprove , for any prime p2 there exist an integer n such that :- n(n+1)

Question

prove or disprove , for any prime p>2 there exist an integer n such that :-
n(n+1)<p<(n+1)(n+2)

kainui · Answer

Divide both sides by (n+1) and you get n>n+2 so all primes? XD

anonymous · Answer

i'll modify the question

anonymous · Answer

what do u think of it nw :P

kainui · Answer

$$ n(n+1)<p<(n+1)(n+2)$$Ok now divide by (n+1) again and we have $$ n<p<n+2$$ so if we let p=n+1 we have $$n<n+1<n+2$$ which are all consecutive numbers. So to be true, we just pick n=p-1 and this will always work I think.

anonymous · Answer

:P
 yes  was gonna troll by letting u guys trying to find counter example xD

anonymous · Answer

but since u got it fun  is over :P

kainui · Answer

hahaha XD I was unsure cause it seemed easier than it should have been I was trying to find the counter example at first haha.

anonymous · Answer

the inverse though is not true :-
" for any integer n there exist p prime , such that n(n+1)<p<(n+1)(n+2) "

anonymous · Answer

now try to disprove this :P

anonymous · Answer

:D just kidding lol

kainui · Answer

lol XD

anonymous · Answer

ikr :P

anonymous · Answer

so reached what as counter example?

kainui · Answer

lol no idea

kainui · Answer

I think I need to find a gap of 2n+2 composite numbers to find n.

anonymous · Answer

the thing is as n become bigger the gap btw 
n(n+1) and (n+1)(n+2) become bigger :D
so sometimes we even have many primes btw 
think of it , i'll go and study :P
good night :D

kainui · Answer

Haha yeah it's a big problem. I'll see what I can do. =D

ganeshie8 · Answer

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