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Find integers a, b, d, s, t such that all of the following hold
(1) a > 0, b > 0,
(2) d = sa + tb, and
(3) d =/= gcd(a, b).
I think that d cannot exist, since, by Bezout's lemma, (2)
~(3). I was just wondering if I was right?Last edited by Identity (2007-09-18 23:32:37)
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(2) restricts d to be a multiple of the gcd, but not necessarily the gcd itself.
There are infinite solutions to this.
One would be a=2, b=3, d=5, s=t=1.
Why did the vector cross the road?
It wanted to be normal.
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As a simple example, you can take a = b = 1, and s and t any positive integers you like.
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i forgot to say thanks, thanks!
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