I have tried to solve this problem:

714x + 7007y = 7

but I have not come to a solution yet.

Thank you!

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- Mar 15th 2007, 01:44 PMjmc1979Linear Combination
I have tried to solve this problem:

714x + 7007y = 7

but I have not come to a solution yet.

Thank you! - Mar 15th 2007, 02:15 PMThePerfectHacker
Let us find the greatest common divisor by the algorithm mentioned in the Elements.

7007=(9)714+581

714=(1)581+133

581=(4)133+49

133=(2)49+35

49=(1)35+14

35=(2)14+7

14=(2)7+0

Work backwards.

7=35-2*14

7=35-2(49-35)=3*35-2*49

7=3(133-2*49)-2*49

7=3*133-8*49

7=3*133-8(581-4*133)=35*133-8*581

7=35(714-581)-8*581=35*714-43*581

7=35*714-43(7007-9*714)=422*714-43*7007

Thus,

714x+7007y=7

Say for example,

x=422 and y=-43 - Mar 15th 2007, 02:22 PMjmc1979Thank you!
Thank you "The Perfect Hacker"!

- Mar 15th 2007, 02:35 PMfrenzy
how about...

x=1001*n+422

y=-102*n-43

n and integer

:) - Mar 15th 2007, 02:39 PMjmc1979Thanx
Thank you!