Magische Quadrate aus siebten Potenzen
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Magic squares of 7th powers are known since 2004-2005, using very big 65536 x 65536 heptamagic squares, durch direktes Erheben der Zahlen in die 7. Potenz.
Aber ist es möglich, kleinere Quadrate aus 7. Potenzen zu konstruieren?? Hopefully, yes! In 2012 and 2013, using similar methods than those already used for squares of 6th powers, Jaroslaw Wroblewski und Toshihiro Shirakawa constructed these squares:
Square |
Ordnung |
Date |
Author |
S7 |
max. Zahl |
Semi-magisch |
März 2012 |
Jaroslaw Wroblewski |
3,54e+375 |
(3,81e+53)^7 |
|
April 2013 |
Toshihiro Shirakawa |
1,97e+250 |
(5,59e+35)^7 |
||
Mai 2013 |
3,03e+221 |
(4,20e+31)^7 |
|||
Magisch |
September 2013 |
3,14e+51 |
18421557^7 |
The best known = the smallest known magic and semi-magic are these two
squares below from
Toshihiro Shirakawa.
In his 144x144 magic square, amazing and fun: the 52
digits of S7
are exactly the 52 first digits of the famous number Pi...
YES,
!!!!
But not a coincidence... S7 = T1xT2... and in his construction method,
he chose T1 and T2 for that.
477 |
18574207 |
34679337 |
36262447 |
... |
260857 |
5107 |
36747787 |
39491137 |
... |
632157 |
2830507 |
10097 |
41846587 |
... |
670227 |
6859507 |
5599957 |
11497 |
... |
... |
... |
... |
... |
... |
366770087315531181981431366634007 |
284458648578052236850285053330007 |
229987843531191170219379404820007 |
156149641134335057675262859062007 |
... |
361295906907836686727977167132007 |
280212997106738024359982291340007 |
226555189150128615439985682360007 |
153819049475613638903990279076007 |
... |
333925004869364210460706169622007 |
258984739750166961908468481390007 |
209391917244815841543017070060007 |
142166091182006545047627379146007 |
... |
303817012627044486566708072361007 |
235633656657938793211803290445007 |
190512318148971790256351596530007 |
129347837059038741805628189223007 |
... |
... |
... |
... |
... |
... |
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