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Math Help - Linear combination please help

  1. #1
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    Linear combination please help

    gcd (42,660 )

    660 = 41*16 + 4
    41 = 4 * 10 + 1
    4 = 1 * 4 + 0

    so gcd ( 42, 660 ) = 1

    How do express it as linear combination of 41 and 660. I know i work backward....and i get this far and i get stuck..

    1 = 41-4*10
    1 = 41-(660-41*16)*10

    After that...i have no idea what to. I have been reading the examples and problems people have done on this site but i just can't figure out where their numbers are coming from. Any help would be appreciated...Thank you
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  2. #2
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    Quote Originally Posted by smoothi963 View Post
    gcd (42,660 )

    660 = 41*16 + 4
    41 = 4 * 10 + 1
    4 = 1 * 4 + 0

    so gcd ( 42, 660 ) = 1
    No wonder you cannot get the right answer, you got the greatest commond divisor all wrong.

    Watch frum die meister und lern.

    660=15*42+30
    42=1*30+12
    30=2*12+6
    12=2*6+0
    Thus, gcd(42,660)=6.

    Now linear combinations:

    30-2*12=6
    30-2(42-30)
    30-2*42+2*30=3*30-2*42=6
    3(660-15*42)-2*42=6
    3*660-47*42=6
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  3. #3
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    thank you

    Thank you....lol i am so retarded. >.<
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