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

Home > Just Math
How many perfect squares (Posted on 2006-04-25) Difficulty: 3 of 5
Suppose a and b are positive integers. We all know that aČ+2ab+bČ is a perfect square. Give an example where also aČ+ab+bČ is a perfect square. How many such examples exist?

See The Solution Submitted by Salil    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Partial Solution | Comment 3 of 19 |
(In reply to re: Partial Solution by Charlie)

Here's just the beginning of what seems a never-ending list of the beginnings of families of solutions. The only member of the family shown is the one in which the gcd of the two numbers is 1.

3       5
7       8
5       16
11      24
7       33
13      35
16      39
9       56
32      45
17      63
40      51
11      85
19      80
55      57
40      77
24      95
13      120
23      120
65      88
69      91
25      143
56      115
15      161
75      112
32      175
104     105
56      165
29      195
17      208
87      160
85      168
31      224
119     145
72      203
19      261
93      187
64      221
144     155
95      217
40      279
  10   T=3
  20   while (Ct<40)
  30    for I=1 to int(T/2)
  40     J=T-I
  50     if gcd(I,J)=1 then
  60       :V=I*I+I*J+J*J
  70       :Sr=int(sqrt(V)+0.5)
  80       :if Sr*Sr=V then print I,J:Ct=Ct+1:endif
  90    next
  95    T=T+1
 100   wend

  Posted by Charlie on 2006-04-25 10:05:05
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 (3)
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