Talk:2601 as Sum of 3 Squares in 12 Different Ways

There are actually $12$, he missed:
 * $51^2 = 3^2 + 36^2 + 36^2 = 14^2 + 31^2 + 38^2$

The original question by John M. Howell, Littlerock, CA asked for squares that can be expressed as sum of three squares in two different ways.

$51$ is one of the 'other solutions by many readers'. (JRM 22:1 p.75, but the whole solution is contained in p.74-76) --RandomUndergrad (talk) 07:05, 10 July 2020 (UTC)


 * Now I have a partially-complete list of the contents of JRM assembled piecemeal from Ashbacher's blog, but that's as far as it goes. This list does not give the page numbers, just the article titles and their authors. I do not have access to the actual magazines themselves, so I can't find out what the article in question is called (although in this case I am assuming it's probably "Problems and Conjectures" or "Solutions to Problems and Conjectures", or something like that.


 * So:
 * a) Was this solution complete in JRM 22:1 p.74-76? That is, is the omission due to Wells, or due to JRM?
 * b) What's the date of this issue?
 * c) What's the title of the article it's in?


 * Then I will be able to complete the work to cite this result and to craft the erratum page as appropriate.


 * It may be silly of me to make such a fuss of the citations, but it's the OCD in me trying to present a consistent front for this website. --prime mover (talk) 07:19, 10 July 2020 (UTC)


 * a) 12 solutions are in JRM. I didn't check if they are all of them, though it shouldn't take long.
 * b) Vol. 21 is published in 1989 and Vol. 22. in 1990.
 * c) They are indeed called "Problems and Conjectures" and "Solutions to Problems and Conjectures". The problem in question is 1692, creatively named "Three Squares".
 * --RandomUndergrad (talk) 08:12, 10 July 2020 (UTC)


 * Can you give me the complete citation details for both question and answer? I have so far that the question is in V21 and raised by John M. Howell, but what page(s)? Issue 1? I also don't have the person to whom the answers is to be attributed. Sorry if this is a nuisance, but I want to get this completed. --prime mover (talk) 10:06, 10 July 2020 (UTC)


 * The library is closed, I'll check it next week. However do note that this answer, along with plenty of others, are listed under 'other solutions by many readers', so it is impossible to tell who did it. Also I have verified via a program that all $12$ solutions are accounted for:
 * $\tuple {1, 10, 50}, \tuple {1, 22, 46}, \tuple {1, 34, 38}, \tuple {2, 14, 49}, \tuple {3, 36, 36}, \tuple {10, 10, 49}, \tuple {14, 14,

47}, \tuple {14, 17, 46}, \tuple {14, 31, 38}, \tuple {17, 34, 34}, \tuple {22, 31, 34}, \tuple {24, 27, 36}$ --RandomUndergrad (talk) 11:56, 10 July 2020 (UTC)