c

Let c=2011, C=[1,2,3,...,c], if f does exist

1) f(n+c) = f(n) + c

2) f(a) = f(b) <===> a = b

3) for any n in C, f(n) <= 2c

4) let A and B the subsets of C, so that

   for all a in A, f(a) <= c)

   for all b in B, c<f(b)<=2c

5) B can not be empty.

6) for each b in B, there is an unique a in A, with f(a)=b 

That means A and B have the same number of elements, ...impossible since c is odd!

So, you can not construct any relation for C.

This is true for Cn=[nc+1,nc+2, ... nc+c], n=1,2,3 ......

所有跟帖： 

• What is relation? your 1 to 6 is just my proof. my 2011/2 out of -jinjing- ♀ (255 bytes) () 06/01/2011 postreply 06:51:04

• 回複：What is relation? your 1 to 6 is just my proof. my 2011/2 out -15少- ♂ (133 bytes) () 06/01/2011 postreply 08:31:32

• your (2) means f is bijection function. 1 to 1 and onto. -jinjing- ♀ (78 bytes) () 06/01/2011 postreply 09:03:44

• 回複：your (2) means f is bijection function. 1 to 1 and onto. -15少- ♂ (47 bytes) () 06/01/2011 postreply 09:19:59

• If f is linear, OK. But we can't say nonlinear f is impossible b -jinjing- ♀ (45 bytes) () 06/01/2011 postreply 11:41:54

• you said yourself "for any f, no solution" -15少- ♂ (41 bytes) () 06/01/2011 postreply 13:14:55

• 回複：you said yourself "for any f, no solution" -jinjing- ♀ (55 bytes) () 06/01/2011 postreply 14:28:17

• is there anything wrong in my demonstration 1) to 6)? -15少- ♂ (0 bytes) () 06/01/2011 postreply 15:06:40

• your answer is not math answer, I do this Q, I hope you can see. -jinjing- ♀ (191 bytes) () 06/02/2011 postreply 10:07:19

• MY answer is MY math answer. -15少- ♂ (299 bytes) () 06/02/2011 postreply 12:41:02

• I like the people who like Math. Let me tell you the detail. -jinjing- ♀ (177 bytes) () 06/02/2011 postreply 15:51:05

• 回複：I like math, not myth nor mystification -15少- ♂ (266 bytes) () 06/02/2011 postreply 17:24:06

• You at first you don't think f(N1)=N2,so,I ,,,,your deduce prove -jinjing- ♀ (164 bytes) () 06/02/2011 postreply 18:23:04

• Nice! -亂彈- ♂ (0 bytes) () 06/01/2011 postreply 18:40:26

• thanks! -15少- ♂ (0 bytes) () 06/02/2011 postreply 12:46:16

• 回複：c Could you provide some details for -wxcfan123- ♂ (247 bytes) () 06/11/2011 postreply 18:57:48

• figure out missing details. Nice problem and nice solution. -wxcfan123- ♂ (335 bytes) () 06/12/2011 postreply 14:36:53