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Use the Euclidean algorithm to find integers x and y such that 164x+37y=1. State your answer as a list with x first and y second, separated by a comma.

 Mar 22, 2019
 #1
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164x  +  37y  =  1

164    =   4(37)  + 16

 37   =  2(16) + 5

16 =  3(5) + 1

 

1 =  16 - 3(5)

1 =  16 - 3 [ 37 - 2(16) ]

1 = 7(16) - 3(37)

1 = 7 [ 164 - 4(37)]  - 3(37)

1 = 165 (7)  - 37(28) - 37(3)

1 = 164(7) + 37(-31)

 

So      (x, y)  =  ( 7, -31)

 

 

cool cool cool

 Mar 23, 2019

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