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

Home > Numbers
Single or double (Posted on 2010-12-24) Difficulty: 3 of 5
Both a number N and its half,when augmented by 1 (i.e.N+1 and N/2+1) form a perfect square.
0 is a trivial example.

List 4 more examples.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 1 of 6
   10   for I=1 to 10000000
   20     Sq1=I*I
   30     HalfN=Sq1-1
   40     N=2*HalfN
   50     Sq2=N+1
   60     Sr=int(sqrt(Sq2))
   70     if Sr*Sr=Sq2 then print N,N+1;sqrt(N+1),HalfN+1;sqrt(HalfN+1)
   80   next
finds
 N              N+1 sqrt(N+1)               (N/2)+1  sqrt((N/2)+1)
 0               1  1.0                          1  1.0
 48              49  7.0                         25  5.0
 1680            1681  41.0                      841  29.0
 57120           57121  239.0                    28561  169.0
 1940448         1940449  1393.0                 970225  985.0
 65918160        65918161  8119.0                32959081  5741.0
 2239277040      2239277041  47321.0             1119638521  33461.0
 76069501248     76069501249  275807.0           38034750625  195025.0
 2584123765440   2584123765441  1607521.0        1292061882721  1136689.0
 87784138523760  87784138523761  9369319.0       43892069261881  6625109.0
 

  Posted by Charlie on 2010-12-24 17:29:45
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 (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information