let a^2+4*a*b+b^2=(a+2*b)^2-3b^2=t^2-3*b^2;
if x=t1^2-3*b1^2, y==t2^2-3*b2^2;
so x*y=(t1^2-3*b1^2)*(t2^2-3*b2^2)=(t1*t2+3*b1*b2)^2-3*(t1*b2+t2*b1)^2;
so x*y also belongs to A
let a^2+4*a*b+b^2=(a+2*b)^2-3b^2=t^2-3*b^2;
if x=t1^2-3*b1^2, y==t2^2-3*b2^2;
so x*y=(t1^2-3*b1^2)*(t2^2-3*b2^2)=(t1*t2+3*b1*b2)^2-3*(t1*b2+t2*b1)^2;
so x*y also belongs to A
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回复:回复:有没有好办法?
-cma-
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(48 bytes)
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03/11/2012 postreply
15:49:44
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SORRY,LAST IS NOT RIGHT。
-jinjing-
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03/11/2012 postreply
16:05:20
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Great! This is related to Pell's equation etc.
-乱弹-
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03/11/2012 postreply
19:33:45
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