All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
2*P + 2 = Perfect Square? (Posted on 2010-05-01) Difficulty: 4 of 5
Each of P and Q is a nonnegative integer satisfying the equation: P2 = 28*Q2 + 1

Is 2*P + 2 always a perfect square?

If so, prove it. Otherwise, provide a counterexample.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts a computerized start but no proof and too small a sample size | Comment 1 of 5
list
   10   for Q=0 to 10000000
   20   P2=28*Q*Q+1
   30   P=int(sqrt(P2)+0.5)
   40   if P*P=P2 then
   50     :Perfsq=2*P+2
   60     :Sr=sqrt(Perfsq)
   70     :print Q;P,Perfsq;Sr
   80   next
OK
 Q        P         2P+2      Sqrt(2P+2)
 0  1    4   2.0
 24  127       256  16.0
 6096  32257     64516  254.0
 1548360  8193151   16386304  4048.0

Every entry in column 3 is a perfect square, giving some credibility to the assertion, but not even a statistical proof.


  Posted by Charlie on 2010-05-01 16:12:05
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information