L05_exgcd_print

L05_exgcd_print - = 99 , j = 63 1) First run the regular...

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1 i k [ i ] = j [ i ] q [ i ] + r [ i ] k [ i ] j [ i ] r [ i ] q [ i ] y [ i ] x [ i ] 0 184 = 69(2) + 46 184 69 46 2 - 1 3 1 69 = 46(1) + 23 69 46 23 1 1 - 1 2 46 = 23(2) + 0 46 23 0 2 0 1 Recall that (**) y [ i - 1] = x [ i ] and (*) x [ i - 1] = y [ i ] - q [ i - 1] x [ i ] Example: k = 184 , j = 69 1) First run the regular GCD algorithm: get gcd (184 , 69) = 23 2) Then calculate y [2] = 0 , x [2] = 1 3) Continue bottom-up, calculating the x [ i ] , y [ i ] from (*) and (**) 4) We are done! Note that 184( - 1) + 69(3) = 23 = gcd (184 , 69) . and we want j [ i ] x [ i ] + k [ i ] y [ i ] = gcd ( k [ i ] , j [ i ])
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2 i k [ i ] = j [ i ] q [ i ] + r [ i ] k [ i ] j [ i ] r [ i ] q [ i ] y [ i ] x [ i ] 0 99 = 63(1) + 36 99 63 36 1 2 - 3 1 63 = 36(1) + 27 63 36 27 1 - 1 2 2 36 = 27(1) + 9 36 27 9 1 1 - 1 3 27 = 9(3) + 0 27 9 0 3 0 1 Recall that (**) y [ i - 1] = x [ i ] and (*) x [ i - 1] = y [ i ] - q [ i - 1] x [ i ] Example: k
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Unformatted text preview: = 99 , j = 63 1) First run the regular GCD algorithm: get gcd (99 , 63) = 9 2) Then calculate y [3] = 0 , x [3] = 1 3) Continue bottom-up, calculating the x [ i ] , y [ i ] from (*) and (**) 4) We are done! Note that 99(2) + 63(-3) = 9 = gcd (99 , 63) . and we want j [ i ] x [ i ] + k [ i ] y [ i ] = gcd ( k [ i ] , j [ i ])...
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L05_exgcd_print - = 99 , j = 63 1) First run the regular...

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