1729 la so tu nhien lien sau 1728 va lien truoc 1730. No con đuoc biet la so Hardy-Ramanujan, sau cau chuyen cua nha toan hoc Anh G. H. Hardy khi ong tham nha toan hoc An Đo Srinivasa Ramanujan o benh vien. Ong ke lai cuoc tro chuyen:

Toi nho mot lan đen tham khi anh ay bi benh o Putney. Toi đi tren chiec taxi mang so 1729 va noi rang con so nay co ve buon te voi toi, va toi mong rang no khong phai la mot điem bao xui xeo. "Khong," anh ay tra loi, "no la mot con so rat thu vi; no la so nho nhat co the bieu dien duoi dang tong hai lap phuong bang hai cach khac nhau."

Hai cach đo la:

1729 = 13 + 123 = 93 + 103
Khi trich co nguoi su dung cum tu "so lap phuong duong", vi neu tinh so lap phuong am (lap phuong cua so nguyen am) thi nghiem nho nhat la 91 (la mot uoc cua 1729):

91 = 63 + (−5)3 = 43 + 33
Nhung so nho nhat co the bieu dien duoi dang tong cua hai so lap phuong bang n cach khac nhau đuoc goi la "so taxi". Con so nay cung xuat hien trong tap cua Ramanujan nhieu nam truoc vu tai nan, va đuoc chu y boi Frenicle de Bessy nam 1657.
Bieu dien tuong tu đinh nghia 1729 la so đau tien cua day "Fermat gan đung" (day so A050794 trong bang OEIS) lien quan toi Đinh ly lon Fermat, la nhung so dang 1 + z3 va cung bang tong cua hai lap phuong khac.


Tinh chat khac 1729 cung la so Carmichael va la so gia nguyen to Euler tuyet đoi đau tien. No cung la tich cua ba so nguyen to.
1729 la mot so Zeisel. No la mot so lap phuong chinh giua, mot so thap nhi giac đeu, mot so 24-giac đeu va so 84-giac đeu.
Do trong he thap phan 1729 chia het cho tong cac chu so cua no, 1729 la mot so Harshad. No cung co tinh chat nay trong he bat phan (1729 = 33018, 3 + 3 + 0 + 1 = 7) and hexadecimal (1729 = 6C116, 6 + C + 1 = 1910), nhung khong co trong he nhi phan va he thap nhi phan.
Trong he thap nhi phan, 1729 co dang 1001, nen nghich đao cua no co chu ky la 6 trong he co so đo
1729 co mot tinh chat thu vi khac: chu so thap phan thu 1729 bat đau cho su xuat hien đau tien lien tiep cua ca 10 chu so khong lap trong bieu dien thap phan cua so sieu viet e.
Masahiko Fujiwara chi ra rang 1729 la mot trong bon so nguyen duong (nhung so khac la 81, 1458, va truong hop hien nhien 1) khi cong cac chu so lai, tao ra mot tong ma khi nhan tong đo voi so viet nguoc lai tong cho ra so ban đau:

1 + 7 + 2 + 9 = 19
19 × 91 = 1729
Đe chung minh, chi can kiem tra nhung tong đong du voi 0 hoac 1 (mod 9) khong vuot qua 19.


Xem them A Disappearing Number, mot vo kich nam 2007 ve Ramanujan tai Anh trong The chien I.
Nghich ly Berry
Nghich ly so thu vi
So taxi
4104, so nguyen duong lon thu hai co the bieu dien thanh tong cua hai lap phuong khac nhau theo hai cach.


Sach tham khao Gardner, Martin (1973), Mathematical Puzzles and Diversions , Pelican / Penguin Books, ISBN 0-14-020713-9
Guy, Richard K. (2004), Unsolved Problems in Number Theory, Problem Books in Mathematics, Vol. 1 (an ban thu 3), Springer, ISBN 0-387-20860-7 - D1 mentions the Hardy–Ramanujan number.


Chu thich Lien ket ngoai MathWorld: Hardy–Ramanujan Number
BBC: A Further Five Numbers Luu tru ngay 19 thang 4 nam 2013 tai archive.today
Grime, James; Bowley, Roger. "1729: Taxi Cab Number or Hardy-Ramanujan Number". Numberphile. Brady Haran. Ban goc luu tru ngay 6 thang 3 nam 2017. Truy cap ngay 17 thang 3 nam 2018.
Mot so su that ve ve đep cua So Ramanujan 1729 (YouTube)
Why does the number 1729 show up in so many Futurama episodes? Luu tru ngay 15 thang 10 nam 2013 tai Wayback Machine, io9.com