the smallest no of this set is $\{24x+60y+2000z: x,y, z \in \mathbb{Z}\}$.and answer option is 2/4/6/24.. i tri this problem to putting the different valus of x,y,z. but i feel this not a right way. any one can help me?
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1You mean the smallest positive integer right ? – T_O Apr 04 '14 at 09:16
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http://math.stackexchange.com/questions/464156/what-is-the-smallest-positive-integer-in-the-set-24x60y2000z-mid-x-y-z-in – lab bhattacharjee Apr 04 '14 at 09:18
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I would guess the smallest number is somewhere around $-\infty$ – Guy Apr 04 '14 at 09:29
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We have $$\gcd(24,60,2000)=4$$ hence by the Bézout's identity there's $x,y,z\in\Bbb Z$ such that $$24x+60y+2000z=4$$