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![[Post New]](/templates/default/images/icon_minipost_new.gif) 7 Apr 2008 11:13:39 IST
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Out of curiosity: The least positive value taken by 21x+12y+15z where  is
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Time wounds all heels |
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7 Apr 2008 11:37:59 IST
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answer is 3 is it not? All are 0 mod 3 and taking 3 out we get 3(7x+4y+5z) Put x=3, y=-5 , z=0 or any such value, so the answer is 3 no?
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7 Apr 2008 11:39:37 IST
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this is a one-liner if you know the concept. I will appreciate an answer backed by solid reasoning
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7 Apr 2008 11:43:18 IST
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GCD of 7,4,5 = 1 are u talking abt that?
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7 Apr 2008 11:47:02 IST
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i meant euclid's algorithm ofc
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7 Apr 2008 11:47:54 IST
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Actually this is one of the definitions of gcd.
The least positive value of ax+by+cz where x,y,z are integers and a,b,c are natural numbers is the gcd of (a,b,c). That is the only thing you need to know for this problem.
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Time wounds all heels |
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7 Apr 2008 11:54:43 IST
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And where from can we learn such definitions? 
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"I a universe of atoms.......an atom in the universe" |
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7 Apr 2008 12:00:11 IST
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From any olympiad book i guess
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7 Apr 2008 12:11:54 IST
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For example ??
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7 Apr 2008 12:18:00 IST
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ya for example?
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23 Apr 2008 12:50:23 IST
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here Z iswhat?
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23 Apr 2008 12:51:28 IST
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how can u find the least value if x,y,z are complex .....there canot b a order relation .... so how the least?
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23 Apr 2008 13:36:53 IST
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guys, you must become familiar with the notation for sets of Natural Numbers (N), Whole Numbers (W), Integers (Z), Rationals (Q), Reals (R) and Complex Numbers (C).
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