5th grader math rocks! problem - r u smarter than a 5th grader?

Prove that the number 3 + 3x3 + 3x3x3 + 3x3x3x3 + .... + 3 to the power of 60 is divisible by 2x2x2x3x5x11x11x13
Hints: 1+3+3x3 = 13; 1+3+3x3+3x3x3 = 40; 1+3+3x3+3x3x3+3x3x3x3 = 121

所有跟帖： 

• 回复：5th grader math rocks! problem - r u smarter than a 5th grade -Jinjing- ♀ (198 bytes) () 02/09/2010 postreply 17:08:48

• brilliant -一用户- ♂ (0 bytes) () 02/09/2010 postreply 19:00:04

• it's harder without the HINT. -pj- ♂ (0 bytes) () 02/12/2010 postreply 06:43:57

• 回复：it's harder without the HINT. -Jinjing- ♀ (32 bytes) () 02/12/2010 postreply 08:22:13

• 回复：5th grader math rocks! problem - r u smarter than a 5th grade -hisch- ♂ (219 bytes) () 02/18/2010 postreply 16:08:33

• Different Proof -hisch- ♂ (0 bytes) () 02/18/2010 postreply 16:10:06