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| Title: | Mathematics at DEC |
|
| Moderator: | RUSURE::EDP |
|
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
112.0. "Triples w same sum & product" by HARE::STAN () Tue Jul 31 1984 19:12
J. G. Mauldon asks how many different triples of positive integers
can you have with the same sum and the same product.
The best anyone has been able to come up with is 5 triples:
( 6, 480, 495)
(11, 160, 810)
(12, 144, 825)
(20, 81, 880)
(33, 48, 900)
Can anyone find 6 such triples?
Reference
Richard K. Guy, Unsolved Problems in Number Theory, Springer-Verlag,
New York: 1981. Page 96, problem D16.
| T.R | Title | User | Personal
Name | Date | Lines |
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| 112.1 | | TOOLS::STAN | | Sat May 25 1985 20:07 | 28 |
| What! No one has bettered the record? Shame.
Lorraine Foster and Gabriel Robins "using a modest computer and various
memory sparing techniques" have found 10 triples that have sum
1326000 and product 2^7 3^6 5^4 7^2 13^3 17^3.
Their 10 triples are:
83300 495720 746980
79968 573750 672282
80325 560235 685440
143325 224640 958035
139230 232050 954720
119340 278460 928200
106080 324870 895050
92820 397800 835380
89505 424320 812175
79560 596700 649740
Consult the follwing reference for the algorithm used:
Reference
---------
Lorraine Foster and Gabriel Robins, Solution to Problem E2872.
American Mathematical Monthly. 89(1982)499-500.
Now with a powerful computer and lots of "memory sparing techniques",
someone should be able to do better than this!
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