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?
(In reply to
re(3): Partial Solution by Charlie)
With regard to base pairs that include a prime, each prime (>=5) seems to be a member of two such base pairs:
5 3
5 16
7 8
7 33
11 24
11 85
13 35
13 120
17 63
17 208
19 80
19 261
23 120
23 385
29 195
29 616
31 224
31 705
37 323
37 1008
41 399
41 1240
43 440
43 1365
47 528
47 1633
53 675
53 2080
59 840
59 2581
61 899
61 2760
67 1088
67 3333
71 1224
71 3745
73 1295
73 3960
79 1520
79 4641
I don't know if composite numbers have a similar theme.
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Posted by Charlie
on 2006-04-25 11:16:22 |
re(4): Partial Solution
