Srinivasa Ramanujan,1887.12.22-1920.4.26,印度著名数学天才， 斯Springer都版的国际数学期刊The Ramanujan Journall即以其名字命名. 从2011年始，每年的12月22日是印度的法定国家假日，2012年被印度政府 确定为印度的国家数学年.印度的数学奖SASTRA Ramanujan Prize和国 际数学奖The Ramanujan Prize以其名字命名.前者获奖年龄限制为32岁以 下，后者45岁以下，奖金分别为10000美元与15000美元 l909年，Ramanujan的第一篇论文发表在Journal of Indian Mathemat- ical Society..在该论文中，他提都以下征解问影： V1+2V1+3v1+.=? 六个月后，没有人能够给都正确答案，Ramanujan.只好自己亲自动手：答 案是3！因为，Ramanujan?发现了下面的恒等式： +n+a=Vax+(n+a)2+zVa(z+n)+(n+a)2+(x+n).. 于是取x=2,n=1,a=0即可. l9l3年，Ramanujan受剑桥大学三一学院教授G.Hardy邀请访问剑桥大 学.期间，Hardy去医院看望Ramanujan.Hardy回忆说： I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one,and that I hoped it was not an unfavorable omen."No,"he replied,"it is a very interesting number;it is the smallest number expressible as the sum of two cubes in two different ways." 课堂练习：请将1729表示成两个正整数的立方和. 17Srinivasa Ramanujan, 1887.12.22õ1920.4.26, ❁Ý❮➯ê➷❯â➜ ❞SpringerÑ❻✛■❙ê➷ÏrThe Ramanujan Journal❂➧Ù➯✐➲➯. ❧2011❝➞➜③❝✛12✛22❋➫❁Ý✛④➼■❬❜❋➜2012❝✚❁Ý✕❄ ✭➼➃❁Ý✛■❬ê➷❝. ❁Ý✛ê➷øSASTRA Ramanujan PrizeÚ■ ❙ê➷øThe Ramanujan Prize➧Ù➯✐➲➯. ❝ö➻ø❝★⑩➏➃32➉➧ ❡➜￾ö45➉➧❡➜ø✼➞❖➃10000④✄❺15000④✄. 1909❝➜Ramanujan✛✶➌➓Ø➞✉▲✸Journal of Indian Mathemat￾ical Society. ✸❚Ø➞➙➜➛❏Ñ➧❡✍✮➥❑➭ r 1 + 2q 1 + 3√ 1 + · · · =? ✽❻✛￾➜✈❦❁❯✡❽Ñ✔✭❽❨➜Ramanujan➄Ð❣❈❾❣➘➹➭❽ ❨➫ 3 ! Ï➃➜Ramanujan✉②✡❡→✛ð✤➟➭ x + n + a = r ax + (n + a) 2 + x q a(x + n) + (n + a) 2 + (x + n) √ · · · ✉➫✒ x = 2, n = 1, a = 0❂➀. 1913❝➜Ramanujan➱ê①➀➷♥➌➷✓✓➬G.Hardy✚➒➊➥ê①➀ ➷. Ï♠➜Hardy✖➎✓✇✧Ramanujan. Hardy↔➪❵➭ I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. ”No,” he replied, ”it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” ➅✱ö❙➭➒ò 1729▲➠↕ü❻✔✒ê✛á➄Ú. 17