Square numbers that use each of the 10 digits exactly once

  

A   is a pandigital square   (containing the digits 0-9)

 
 

         A                   B^2                        A/9                   (B/3)^2

1026753849 \; = \; 32043^2   ……….   114083761 \; = \; 10681^2
1042385796 \; = \; 32286^2   ……….   115820644 \; = \; 10762^2
1098524736 \; = \; 33144^2   ……….   122058304 \; = \; 11048^2
1237069584 \; = \; 35172^2   ……….   137452176 \; = \; 11724^2
1248703569 \; = \; 35337^2   ……….   138744841 \; = \; 11779^2
1278563049 \; = \; 35757^2   ……….   142062561 \; = \; 11919^2
1285437609 \; = \; 35853^2   ……….   142826401 \; = \; 11951^2
1382054976 \; = \; 37176^2   ……….   153561664 \; = \; 12392^2
1436789025 \; = \; 37905^2   ……….   159643225 \; = \; 12635^2
1503267984 \; = \; 38772^2   ……….   167029776 \; = \; 12924^2
1532487609 \; = \; 39147^2   ……….   170276401 \; = \; 13049^2
1547320896 \; = \; 39336^2   ……….   171924544 \; = \; 13112^2
1643897025 \; = \; 40545^2   ……….   182655225 \; = \; 13515^2
1827049536 \; = \; 42744^2   ……….   203005504 \; = \; 14248^2
1927385604 \; = \; 43902^2   ……….   214153956 \; = \; 14634^2
1937408256 \; = \; 44016^2   ……….   215267584 \; = \; 14672^2

2076351489 \; = \; 45567^2   ……….   230705721 \; = \; 15189^2
2081549376 \; = \; 45624^2   ……….   231283264 \; = \; 15208^2
2170348569 \; = \; 46587^2   ……….   241149841 \; = \; 15529^2
2386517904 \; = \; 48852^2   ……….   265168656 \; = \; 16284^2
2431870596 \; = \; 49314^2   ……….   270207844 \; = \; 16438^2
2435718609 \; = \; 49353^2   ……….   270635401 \; = \; 16451^2
2571098436 \; = \; 50706^2   ……….   285677604 \; = \; 16902^2
2913408576 \; = \; 53976^2   ……….   323712064 \; = \; 17992^2

3015986724 \; = \; 54918^2   ……….   335109636 \; = \; 18306^2
3074258916 \; = \; 55446^2   ……….   341584324 \; = \; 18482^2
3082914576 \; = \; 55524^2   ……….   342546064 \; = \; 18508^2
3089247561 \; = \; 55581^2   ……….   343249729 \; = \; 18527^2
3094251876 \; = \; 55626^2   ……….   343805764 \; = \; 18542^2
3195867024 \; = \; 56532^2   ……….   355096336 \; = \; 18844^2
3285697041 \; = \; 57321^2   ……….   365077449 \; = \; 19107^2
3412078569 \; = \; 58413^2   ……….   379119841 \; = \; 19471^2
3416987025 \; = \; 58455^2   ……….   379665225 \; = \; 19485^2
3428570916 \; = \; 58554^2   ……….   380952324 \; = \; 19518^2
3528716409 \; = \; 59403^2   ……….   392079601 \; = \; 19801^2
3719048256 \; = \; 60984^2   ……….   413227584 \; = \; 20328^2
3791480625 \; = \; 61575^2   ……….   421275625 \; = \; 20525^2
3827401956 \; = \; 61866^2   ……….   425266884 \; = \; 20622^2
3928657041 \; = \; 62679^2   ……….   436517449 \; = \; 20893^2
3964087521 \; = \; 62961^2   ……….   440454169 \; = \; 20987^2
3975428601 \; = \; 63051^2   ……….   441714289 \; = \; 21017^2
3985270641 \; = \; 63129^2   ……….   442807849 \; = \; 21043^2

 
Find other pandigital squares.
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged , . Bookmark the permalink.

One Response to Square numbers that use each of the 10 digits exactly once

  1. Paul says:

    doesn’t seem to want to post the list, so they are here

    https://www.dropbox.com/s/3zi9ra50zlkzkhh/sqrs.txt?dl=0

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