n-digit numbers whose cubes end with the same n digits

 
 
1-digit :

4^3   =   64
6^3   =   216
9^3   =   729
 
2-digit :

24^3   =   13824
25^3   =   15625
49^3   =   117649
76^3   =   438976
 
3-digit :

125^3   =   1953125
249^3   =   15438249
251^3   =   15813251
375^3   =   52734375
376^3   =   53157376
499^3   =   124251499
501^3   =   125751501
624^3   =   242970624
625^3   =   244140625
749^3   =   420189749
751^3   =   423564751
875^3   =   669921875
999^3   =   997002999

 
4-digit :

0624^3   =   242970624
0625^3   =   244140625
1249^3   =   1948441249
3751^3   =   52776573751
4375^3   =   83740234375
4999^3   =   124925014999
5001^3   =   125075015001
5625^3   =   177978515625
6249^3   =   244023456249
8751^3   =   670151588751
9375^3   =   823974609375
9376^3   =   824238309376
9999^3   =   999700029999

 
5-digit :

09375^3   =   823974609375
09376^3   =   824238309376
18751^3   =   6592851618751
31249^3   =   30514648531249
40625^3   =   67047119140625
49999^3   =   124992500149999
50001^3   =   125007500150001
59375^3   =   209320068359375
68751^3   =   324965351768751
81249^3   =   536357148681249
90624^3   =   744268574490624
90625^3   =   744293212890625
99999^3   =   999970000299999

 
6-digit :

109375^3   =   1308441162109375
109376^3   =   1308477051109376
218751^3   =   10467672852218751
281249^3   =   22247077149281249
390625^3   =   59604644775390625
499999^3   =   124999250001499999
500001^3   =   125000750001500001
609375^3   =   226284027099609375
718751^3   =   371308922853718751
781249^3   =   476835327150781249
890624^3   =   706452851076890624
999999^3   =   999997000002999999

 
7-digit :

0781249^3   =   476835327150781249
2109375^3   =   9385585784912109375
2890624^3   =   24153207507332890624
2890625^3   =   24153232574462890625
4218751^3   =   75084739672864218751
4999999^3   =   124999925000014999999
5000001^3   =   125000075000015000001
5781249^3   =   193225760327165781249
7109375^3   =   359330654144287109375
7109376^3   =   359330805773947109376
7890625^3   =   491285800933837890625
9218751^3   =   783458964672879218751
9999999^3   =   999999700000029999999

 
8-digit :

12890624^3   =   2142011620788612890624
12890625^3   =   2142012119293212890625
24218751^3   =   14205457539672924218751
25781249^3   =   17136094960327225781249
37109375^3   =   51103532314300537109375
49999999^3   =   124999992500000149999999
50000001^3   =   125000007500000150000001
62890625^3   =   248746931552886962890625
74218751^3   =   408828275039673074218751
75781249^3   =   435196382460327375781249
87109375^3   =   660989701747894287109375
87109376^3   =   660989724512024187109376
99999999^3   =   999999970000000299999999

 
9-digit :

074218751^3   =   408828275039673074218751
212890624^3   =   9648717803886414212890624
212890625^3   =   9648717939853668212890625
287109375^3   =   23666940629482269287109375
425781249^3   =   77189742974960328425781249
499999999^3   =   124999999250000001499999999
500000001^3   =   125000000750000001500000001
574218751^3   =   189335526025039674574218751
712890625^3   =   362300314009189605712890625
787109375^3   =   487646661698818206787109375
787109376^3   =   487646663557441713787109376
925781249^3   =   793460187724960329925781249
999999999^3   =   999999997000000002999999999

 
10-digit :

1425781249^3   =   2898402505974960331425781249
1787109375^3   =   5707598291337490081787109375
1787109376^3   =   5707598300918769841787109376
3212890625^3   =   33165597356855869293212890625
3574218751^3   =   45660786369025039683574218751
4999999999^3   =   124999999925000000014999999999
5000000001^3   =   125000000075000000015000000001
6425781249^3   =   265324778730974960346425781249
6787109375^3   =   312647200189530849456787109375
8212890624^3   =   553972386552694511438212890624
8212890625^3   =   553972386755049228668212890625
8574218751^3   =   630352787894025039698574218751
9999999999^3   =   999999999700000000029999999999
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Advertisements

About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles 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