有没有好办法？

 

Let A be the set of all integers of the form a^2+4*a*b+b^2 where a and b are integers,

How can I prove that if x, y belong to A, x*y also belongs to A?

 

Thanks in advance 

所有跟帖： 

• Maybe I am wrong. An Counterexample. -wxcfan123- ♂ (304 bytes) () 03/11/2012 postreply 12:04:18

• 回复：Maybe I am wrong. An Counterexample. -cma- ♂ (163 bytes) () 03/11/2012 postreply 13:04:23

• ＨＩ，Ｘ＝１９，Ｙ＝－１。 -jinjing- ♀ (0 bytes) () 03/11/2012 postreply 15:30:43

• 回复：有没有好办法？ -万斤油- ♂ (206 bytes) () 03/11/2012 postreply 15:03:31

• 回复：回复：有没有好办法？ -cma- ♂ (48 bytes) () 03/11/2012 postreply 15:49:44

• ＳＯＲＲＹ，ＬＡＳＴ　ＩＳ　ＮＯＴ　ＲＩＧＨＴ。 -jinjing- ♀ (0 bytes) () 03/11/2012 postreply 16:05:20

• Great! This is related to Pell's equation etc. -乱弹- ♂ (0 bytes) () 03/11/2012 postreply 19:33:45

• ＴＨＥ Q IS　ＷＲＯＮＧ， -jinjing- ♀ (478 bytes) () 03/11/2012 postreply 15:20:33

• I don't think so: 回复：ＴＨＥ Q IS　ＷＲＯＮＧ， -万斤油- ♂ (74 bytes) () 03/11/2012 postreply 17:31:57

• THANKS,PLESE TRY THIS;XX+4XY+YY=69,NO SOLUTION. -jinjing- ♀ (51 bytes) () 03/11/2012 postreply 19:29:43

• Here is another more direct proof so that you can check the prob -aisanguo- ♀ (235 bytes) () 03/11/2012 postreply 19:56:30

• I'M WRONG,YOU ALSO WRONG.I'LL DO IT BY PEN TOMORROW. -jinjing- ♀ (0 bytes) () 03/11/2012 postreply 20:40:24

• Thanks for pointing it out. It seems just a typo. -AiSanGuo- ♀ (0 bytes) () 03/11/2012 postreply 21:50:35

• Sorry, there is a typo: u should be a*c-b*d -AiSanGuo- ♀ (0 bytes) () 03/11/2012 postreply 21:13:05

• F(2,5)=69 or F(-2,-5)=69, I think the Q is right. -万斤油- ♂ (0 bytes) () 03/11/2012 postreply 20:03:06

• 回复：ＴＨＥ Q IS　ＷＲＯＮＧ， -万斤油- ♂ (214 bytes) () 03/11/2012 postreply 17:55:24

• f(a,b)*f(c,d)=(ac-bd+ad+bc+4bd)^2 + 2(ac-bd)(ad+bc+4cd) -jinjing- ♀ (87 bytes) () 03/14/2012 postreply 11:16:15

• f(a,b)*f(c,d)=(ac-bd+ad+bc+4bd)^2 + 2(ac-bd)(ad+bc+4bd) -jinjing- ♀ (19 bytes) () 03/14/2012 postreply 11:20:29

• Too old to be right. 2(F+G) should be 2F*G. -jinjing- ♀ (0 bytes) () 03/14/2012 postreply 12:23:28