Thanks for your Q. I can do.

1) 9781 is Prime number.

2)Y is not 0,let y=Pi1^a1*Pi2^a2*...Pim^am

3)We have (x+1)(x-1)=9781y^2=(9781Pi1^t1*...Pim^tm)(Pi1^s1*...Pim^sm),...

4)(x+1)-(x-1)=2=1*2=(9781Pi1^c1*...Pim^cm-Pi1^d1*...Pim^dm)*Pi1^e1*...Pim^em

  So,Pi1=2,The right >=4. Contradiction, no solution if y>0.

所有跟帖： 

• For srict logic,though it is trivial, | y^2--9781|=2 no intg. so -jinjing- ♀ (0 bytes) () 01/26/2011 postreply 10:28:12

• 回复：Thanks for your Q. I can do. -calligraphy- ♂ (681 bytes) () 01/26/2011 postreply 12:20:42

• We only check |y^2-P|=2,If there is no solution,the Q has no who -jinjing- ♀ (298 bytes) () 01/26/2011 postreply 16:50:24

• (n^2+1)^2-(n^2+2)*n^2=1,(n^2-1)^2-(n^2-2)*n^2=1.If for any coeff -jinjing- ♀ (229 bytes) () 01/26/2011 postreply 19:08:09

• 回复：(n^2+1)^2-(n^2+2)*n^2=1,(n^2-1)^2-(n^2-2)*n^2=1.If for any co -calligraphy- ♂ (511 bytes) () 01/26/2011 postreply 20:47:19

• Your Ex,5should be 5^2m,3 ...3^2n...,We get |9781-Z^2|=1, -jinjing- ♀ (344 bytes) () 01/27/2011 postreply 09:35:02

• 回复：Your Ex,5should be 5^2m,3 ...3^2n...,We get |9781-Z^2|=1, -calligraphy- ♂ (425 bytes) () 01/27/2011 postreply 11:26:44

• 回复：回复：Your Ex,5should be 5^2m,3 ...3^2n...,We get |9781-Z^2|=1, -jinjing- ♀ (438 bytes) () 01/27/2011 postreply 17:19:24

• 回复：We only check |y^2-P|=2,If there is no solution,the Q has no -calligraphy- ♂ (162 bytes) () 01/27/2011 postreply 07:03:34

• 回复：We only check |y^2-P|=2,If there is no solution,the Q has no -calligraphy- ♂ (3010 bytes) () 01/27/2011 postreply 07:11:39

• 回复：We only check |y^2-P|=2,If there is no solution,the Q has no -calligraphy- ♂ (380 bytes) () 01/27/2011 postreply 07:48:25

• 回复：We only check |y^2-P|=2,If there is no solution,the Q has no -calligraphy- ♂ (201 bytes) () 01/27/2011 postreply 08:21:54

• "So,Pi1=2,The right >=4. Contradiction, no solution if y>0",It i -jinjing- ♀ (0 bytes) () 01/28/2011 postreply 09:09:19