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 How many perfect squares (Posted on 2006-04-25)
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)

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 re(4): Partial Solution | Comment 7 of 19 |
(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       35       167       87       3311      2411      8513      3513      12017      6317      20819      8019      26123      12023      38529      19529      61631      22431      70537      32337      100841      39941      124043      44043      136547      52847      163353      67553      208059      84059      258161      89961      276067      108867      333371      122471      374573      129573      396079      152079      4641`

I don't know if composite numbers have a similar theme.

 Posted by Charlie on 2006-04-25 11:16:22

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