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Algebra

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7 Apr 2008 11:13:39 IST

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707

Minimum Value

None

Out of curiosity: The least positive value taken by 21x+12y+15z where x,y,z in mathbb{Z} is

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sandeep ramesh

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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?

Hari Shankar

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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

sandeep ramesh

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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?

sandeep ramesh

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7 Apr 2008 11:47:02 IST

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i meant euclid's algorithm ofc

Hari Shankar

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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.

Anand Hegde

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7 Apr 2008 11:54:43 IST

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And where from can we learn such definitions? maybe

sandeep ramesh

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7 Apr 2008 12:00:11 IST

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From any olympiad book i guess

Harsh Shukla

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7 Apr 2008 12:11:54 IST

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For example ??

Anand Hegde

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7 Apr 2008 12:18:00 IST

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ya for example?

abhishek gupta

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23 Apr 2008 12:50:23 IST

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here Z iswhat?

abhishek gupta

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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?

Hari Shankar

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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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