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Conference rusure::math

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

330.0. "Pitag. Quads" by TAV02::NITSAN () Thu Aug 29 1985 04:17

                   2   2   2
We all know that  3 + 4 = 5 .

                         3   3   3   3
Did you know that also  3 + 4 + 5 = 6  ?


Any other "funny" combinations like this? Any special reason for this?
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330.1METOO::YARBROUGHThu Aug 29 1985 13:2422
This is a special case of the identity

 3  3  3 3    3  3  3 3    3  3   3 3    3   3  3 3
a (a +b )  = b (a +b )  + a (a -2b )  + b (2a -b ) 
                                        3
for a = 2, b = 1 (divide the result by 3 ).

A similar identity is:

 3  3   3 3     3  3  3 3    3  3  3 3    3   3  3 3
a (a +2b )   = a (a -b )  + b (a -b )  + b (2a +b )

I like the following relationship:
 n   n   n   n   n    n    n    n    n  n   n   n   n    n    n    n 
1 +13 +28 +70 +82 +124 +139 +151  = 4 +7 +34 +61 +91 +118 +145 +148
for n = 1...7

All of this is from "Recreations in the Theory of Numbers" by A. H. Beiler,
published by Dover in 1964. Great book for people like us.

Lynn Yarbrough
     
330.2ADVAX::J_ROTHThu Aug 29 1985 20:509
I was about to post a similar reply...

I had Beiler for freshman caclulus in 1967, he was an interesting
character; I didn't find out about his book until quite a bit later
though.

I don't know if he's still living, he was quite old at the time.

- Jim