Sum Of Squares & 9-digit Square Num3ers w/ digits from 1 to 9 #mathchat

Here’s a list of 9-digit numbers (containing digits from 1 to 9) that have 1 or more representations as a sum of 2 squares.

For example, the two numbers 1596 and 24837 contain all digits from 1 to 9 only once, and the result 619423785 contain all digits 1 to 9 used only once.
1596^2 + 24837^2 = 619423785 = 16179^2 + 18912^2

1635^2 + 29487^2 = 872156394
= 8565^2 + 28263^2 = 11415^2 + 27237^2 = 17535^2 + 23763^2

1875^2 + 24693^2 = 613259874 = 15207^2 + 19545^2

2367^2 + 19485^2 = 385267914

2436^2 + 18975^2 = 365984721 = 6780^2 + 17889^2

2538^2 + 17649^2 = 317928645
= 2943^2 + 17586^2 = 5598^2 + 16929^2 = 5679^2 + 16902^2
= 6066^2 + 16767^2 = 8559^2 + 15642^2 = 9774^2 + 14913^2
= 12303^2 + 12906^2

2784^2 + 15369^2 = 243956817
= 1311^2+ 15564^2 = 4776^2 + 14871^2 = 8481^2 + 13116^2

2943^2 + 17586^2 = 317928645
= 2538^2 + 17649^2 = 5598^2 + 16929^2 = 5679^2 + 16902^2
= 6066^2 + 16767^2 = 8559^2 + 15642^2 = 9774^2 + 14913^2
= 12303^2 + 12906^2

3495^2 + 12768^2 = 175236849

3516^2 + 28479^2 = 823415697
= 12036^2 + 26049^2 = 14199^2 + 24936^2 = 19416^2 + 21129^2

3654^2 + 12897^2 = 179684325
= 1422^2 + 13329^2 = 2367^2 + 13194^2 = 4815^2 + 12510^2
= 7119^2 + 11358^2 = 9135^2 + 9810^2

3846^2 + 29175^2 = 865972341
= 3030^2 + 29271^2 = 7671^2 + 28410^2 = 14055^2 + 25854^2

3864^2 + 25179^2 = 648912537 = 13251^2 + 21756^2

3915^2 + 28467^2 = 825697314 = 7335^2 + 27783^2

3984^2 + 26715^2 = 729563481
= 8880^2 + 25509^2 = 12984^2 + 23685^2 = 17160^2 + 20859^2

4197^2 + 25638^2 = 674921853 = 2667^2 + 25842^2

4359^2 + 16278^2 = 283974165
= 5961^2 + 15762^2 = 9033^2 + 14226^2 = 10407^2 + 13254^2

4395^2 + 27186^2 = 758394621

4536^2 + 12987^2 = 189237465
= 1053^2 + 13716^2 = 7668^2 + 11421^2 = 9072^2 + 10341^2

4698^2 + 21357^2 = 478192653 = 9693^2 + 19602^2

4857^2 + 21396^2 = 481379265
= 7332^2 + 20679^2 = 8952^2 + 20031^2 = 12144^2 + 18273^2

4896^2 + 21753^2 = 497163825 = 9135^2 + 20340^2 = 10791^2 + 19512^2

4965^2 + 17382^2 = 326785149 = 282^2 + 18075^2

4968^2 + 15237^2 = 256847193

5367^2 + 14928^2 = 251649873

5376^2 + 12984^2 = 197485632 = 8184^2 + 11424^2

5376^2 + 18429^2 = 368529417 = 13416^2 + 13731^2

5436^2 + 17289^2 = 328459617

5469^2 + 13728^2 = 218367945 = 7701^2 + 12612^2

5496^2 + 18237^2 = 362794185
= 1941^2 + 18948^2 = 9816^2 + 16323^2 = 11292^2 + 15339^2

5613^2 + 27948^2 = 812596473
= 5568^2 + 27957^2 = 11157^2 + 26232^2 = 19923^2 + 20388^2

5679^2 + 14238^2 = 234971685
= 234^2 + 15327^2 = 3546^2 + 14913^2
= 6111^2 + 14058^2 = 7983^2 + 13086^2
= 9009^2 + 12402^2

5697^2 + 21384^2 = 489731265
= 864^2 + 22113^2 = 2079^2 + 22032^2
= 2808^2 + 21951^2 = 11556^2 + 18873^2
= 13689^2 + 17388^2 = 13959^2 + 17172^2
= 15417^2 + 15876^2

5763^2 + 21948^2 = 514926873
= 3^2 + 22692^2 = 12288^2 + 19077^2 = 15333^2 + 16728^2

5964^2 + 18273^2 = 369471825
= 609^2 + 19212^2 = 5340^2 + 18465^2
= 6807^2 + 17976^2 = 11040^2 + 15735^2
= 11568^2 + 15351^2

5976^2 + 21483^2 = 497231865
= 504^2 + 22293^2 = 8109^2 + 20772^2 = 13779^2 + 17532^2

6189^2 + 25374^2 = 682143597
= 2766^2 + 25971^2 = 7854^2 + 24909^2
= 9474^2 + 24339^2 = 11091^2 + 23646^2
= 12621^2 + 22866^2 = 14106^2 + 21981^2
= 16899^2 + 19914^2

6198^2 + 23547^2 = 592876413 = 13173^2 + 20478^2

6345^2 + 21987^2 = 523687194

6453^2 + 19287^2 = 413629578 = 7443^2 + 18927^2

6459^2 + 17328^2 = 341978265
= 2109^2 + 18372^2 = 9336^2 + 15963^2 = 9987^2 + 15564^2

6471^2 + 23589^2 = 598314762 = 5391^2 + 23859^2

6471^2 + 29538^2 = 914367285
= 999^2 + 30222^2 = 12546^2 + 27513^2 = 17334^2 + 24777^2

6528^2 + 13749^2 = 231649785
= 1716^2 + 15123^2 = 3027^2 + 14916^2
= 4476^2 + 14547^2 = 7701^2 + 13128^2 = 8952^2 + 12309^2

6549^2 + 27831^2 = 817453962
= 2391^2 + 28491^2 = 4659^2 + 28209^2 = 8751^2 + 27219^2

6813^2 + 24597^2 = 651429378 = 13113^2 + 21897^2

6831^2 + 29745^2 = 931427586
= 135^2 + 30519^2 = 4185^2 + 30231^2 = 10719^2 + 28575^2
= 14481^2 + 26865^2 = 17919^2 + 24705^2 = 20025^2 + 23031^2
= 20169^2 + 22905^2

6945^2 + 13782^2 = 238176549
= 1110^2 + 15393^2 = 3018^2 + 15135^2
= 7743^2 + 13350^2 = 8607^2 + 12810^2 = 9345^2 + 12282^2

6975^2 + 14823^2 = 268371954

7164^2 + 25983^2 = 726439185
= 5823^2 + 26316^2 = 16488^2 + 21321^2 = 17559^2 + 20448^2

7356^2 + 24189^2 = 639218457 = 10749^2 + 22884^2

7359^2 + 28146^2 = 846352197

7431^2 + 29658^2 = 934816725
= 11850^2 + 28185^2 = 15438^2 + 26391^2

7458^2 + 23619^2 = 613478925
= 6051^2 + 24018^2 = 8205^2 + 23370^2
= 9570^2 + 22845^2 = 12534^2 + 21363^2 = 13773^2 + 20586^2

7659^2 + 13248^2 = 234169785 = 6003^2 + 14076^2

7659^2 + 13428^2 = 238971465
= 1251^2 + 15408^2 = 1548^2 + 15381^2 = 5112^2 + 14589^2
= 6147^2 + 14184^2 = 8244^2 + 13077^2 = 8604^2 + 12843^2
= 10467^2 + 11376^2

7824^2 + 19356^2 = 435869712

7863^2 + 21495^2 = 523861794 = 2625^2 + 22737^2

7869^2 + 23514^2 = 614829357

7953^2 + 16824^2 = 346297185
= 48^2 + 18609^2 = 3567^2 + 18264^2 = 3732^2 + 18231^2
= 7113^2 + 17196^2 = 9489^2 + 16008^2 = 11127^2 + 14916^2
= 12471^2 + 13812^2

8259^2 + 13476^2 = 249813657 = 8004^2 + 13629^2

8295^2 + 14763^2 = 286753194
= 987^2 + 16905^2 = 7413^2 + 15225^2 = 10437^2 + 13335^2

8349^2 + 17562^2 = 378129645
= 1482^2 + 19389^2 = 3858^2 + 19059^2 = 12819^2 + 14622^2

8352^2 + 17469^2 = 374921865 = 8964^2 + 17163^2

8517^2 + 29643^2 = 951246738 = 19263^2 + 24087^2

8745^2 + 16392^2 = 345172689 = 6600^2 + 17367^2

8793^2 + 12546^2 = 234718965
= 279^2 + 15318^2 = 1206^2 + 15273^2 = 4041^2 + 14778^2
= 4761^2 + 14562^2 = 5634^2 + 14247^2 = 8199^2 + 12942^2
= 9414^2 + 12087^2

8796^2 + 21345^2 = 532978641 = 16320^2 + 16329^2

8796^2 + 23541^2 = 631548297
= 1896^2 + 25059^2 = 3651^2 + 24864^2 = 13749^2 + 21036^2

8934^2 + 15267^2 = 312897645 = 2013^2 + 17574^2

8973^2 + 12546^2 = 237916845
= 4419^2 + 14778^2 = 4653^2 + 14706^2 = 9171^2 + 12402^2

8976^2 + 25413^2 = 726389145
= 2004^2 + 26877^2 = 8067^2 + 25716^2 = 14523^2 + 22704^2

9156^2 + 27483^2 = 839147625
= 51^2 + 28968^2 = 420^2 + 28965^2 = 1104^2 + 28947^2
= 3813^2 + 28716^2 = 4380^2 + 28635^2 = 4845^2 + 28560^2
= 5880^2 + 28365^2 = 7707^2 + 27924^2 = 8160^2 + 27795^2
= 9165^2 + 27480^2 = 10149^2 + 27132^2 = 12315^2 + 26220^2
= 12648^2 + 26061^2 = 13260^2 + 25755^2 = 13587^2 + 25584^2
= 13677^2 + 25536^2 = 16485^2 + 23820^2 = 17043^2 + 23424^2
= 17340^2 + 23205^2 = 17715^2 + 22920^2 = 19164^2 + 21723^2
= 19941^2 + 21012^2 = 20280^2 + 20685^2

9168^2 + 23475^2 = 635127849 = 5268^2 + 24645^2

9627^2 + 18543^2 = 436521978
= 2103^2 + 20787^2 = 5817^2 + 20067^2 = 12813^2 + 16503^2

9687^2 + 24513^2 = 694725138

9735^2 + 24861^2 = 712839546
= 1425^2 + 26661^2 = 11289^2 + 24195^2 = 17355^2 + 20289^2

9741^2 + 26358^2 = 789631245
= 1146^2 + 28077^2 = 8022^2 + 26931^2 = 17763^2 + 21774^2

Advertisements

About benvitalis

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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s