Recent content by johnny009

n^2 - 14n + 40, is this quadratic composite or prime - when n ≤ 0. Determine, all integer values of 'n' - for which n^2 - 14n + 40 is prime? Proof Required. ps. I can do the workings, but the 'proof' is the problem. Many Thanks John.

Dear ALL, My last Question of the Day? Let b1 and b2 be a sequence of numbers defined by: $$b_{n}=b_{n-1}+2b_{n-2}$$ where $b_1=1,\,b_2=5$ and $n\ge3$ a) Write out the 1st 10 terms. b) Using strong Induction, show that: $$b_n=2^n+(-1)^n$$ [FONT=garamond]Many Thanks John C.

Hi There, My apologies, there was an error...in a previous question, which I POSTED ....last week. This question has now been withdrawn, & replaced with the following : ----------------------------------------------------------------------------------------------------------------- a) Show...

--------------------------------------------------------------------------------------------- Hi There, Thanks a lot for the reply. But, your solutions ignores the fact, that 'm' cannot be less than 'N' ...as per the QUESTION?? So, your solution...is not really addressing the Question...

if n is a positive integer greater than 2 and m the smallest integer greater than or = n, that is a perfect square. Let a = m-n. Show that if n is prime, then a is not a perfect square. Also, is the converse of above true, for any integer n? any guidance, will be much appreciated? Thanks