Back to [Numbers 120-129]

 

[Math.]  121 = 112 = 30+31+32+33+34. (Fermat).

The only other non-trivial case: 400 = 202 = 70+71+72+73.

 

[Math.]  One of only 3 known square numbers, which are a factorial plus 1: 25 = 52 = 4!+1, 121 = 112 = 5!+1 and 5041 = 712 = 7!+1. Mathematician Paul Erdös conjectured that these are the only such numbers, called Brown numbers.

 

[Math.]  121 = (12–1)2 = 112.

 

112 = 121 = 23+42+56 = 65+24+32

224 = 234,256 = (2+3+4+2+5+6)4.

 

[Math.]     652562 = 332 , 65+ 56  = 112 and  6556 = 32.

 

[Math.]

121 = 112

121×(1+2+1) = 484 = 222

12,321×(1+2+3+2+1) = 110,889 = 3332

1,234,321×(1+2+3+4+3+2+1) = 19,749,136 = 4,4442

123,454,321×(1+2+3+4+5+4+3+2+1) = 3,086,358,025 = 55,5552

12,345,654,321×(1+2+3+4+5+6+5+4+3+2+1) = 444,443,555,556 = 666,6662

1,234,567,654,321×(1+2+3+4+5+6+7+6+5+4+3+2+1) = 

= 60,493,815,061,729 = 7,777,7772

123,456,787,654,321×(1+2+3+4+5+6+7+8+7+6+5+4+3+2+1) =

= 7,901,234,409,876,544 = 88,888,8882

12,345,678,987,654,321×(1+2+3+4+5+6+7+8+9 +8+7+6+5+4+3+2+1) =  

= 999,999,998,000,000,001 = 999,999,9992.

 

[Math.]

11×11 = 121

112,211×11 = 1,234,321

1,122,332,211×11 = 12,345,654,321

11,223,344,332,211×11 = 123,456,787,654,321

112,233,445,544,332,211×11  =  1,234,567,900,987,654,321

...

 

1×1 = 1

11×11 = 121

111×111 = 12321

1111×1111 = 1234321

11111×11111 = 123454321

111111×111111 = 12345654321

1111111×1111111 = 1234567654321

11111111×11111111 = 123456787654321

111111111×111111111 = 12345678987654321

1111111111×1111111111 = 1234567900987654321.

 

[Math.]  (121+878 = 999 = 101+898)

1212 = 014,641 & 014+641 = 655

8782 = 770,884 & 770+884 = 1654 and 1+654 = 655.

and

1012 = 010,201 & 010+201 = 211

8982 = 806,404 & 806+404 = 1210 and 1+210 = 211

 

120-129

[Library]  Numbers 100-199 are the first 3 digits in Dewey Decimal Classification System call numbers for library books in Philosophy, Psychology and Ethics… Numbers 120-129 are for books in Epistemology and Humankind. 

 

120 (separate page)      

 

121 (separate page)      

 

123 (separate page)