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-- Mar 20 In-Class Exercise Thread

210 858 (d’, x’, y’) = => E( 858, 210 mod 858)

E(210, 18)
 E(18, 12)
 E(12, 6)
 E(6, 0)
 Return (6,1, 0) => (6, 0, 1)
 Return (6,1,-1)
 Return (6, -1, 12)
 Return (6,12, -49)
 Return (6, -49, 12)

(Edited: 2019-03-25)

210 858 (d’, x’, y’) = => E( 858, 210 mod 858) * E(210, 18) *  E(18, 12) *  E(12, 6) *  E(6, 0) *  Return (6,1, 0) => (6, 0, 1) *  Return (6,1,-1) *  Return (6, -1, 12) *  Return (6,12, -49) *  Return (6, -49, 12)

-- Mar 20 In-Class Exercise Thread

Extended-Euclid(6, 0) (6,1,0) Extended-Euclid(12,6) (6,0,1) Extended-Euclid(18,12) (6,1,-1) Extended-Euclid(210,18) (6,-1,12) Extended-Euclid(858,210) (6,12,-49) Extended-Euclid(210,858) (6,-49,12)

At last Result: (6,-49,12)

Extended-Euclid(6, 0) (6,1,0) Extended-Euclid(12,6) (6,0,1) Extended-Euclid(18,12) (6,1,-1) Extended-Euclid(210,18) (6,-1,12) Extended-Euclid(858,210) (6,12,-49) Extended-Euclid(210,858) (6,-49,12) At last Result: (6,-49,12)

-- Mar 20 In-Class Exercise Thread

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-- Mar 20 In-Class Exercise Thread

Extended-Euclid(210,858) - > (6, -49, 12 - floor(210/858) * -49) = (6, -49, 12)

Extended-Euclid(858, 210 MOD 858) -> Extended-Euclid(858, 210) - > (6, 12, -1 - floor(858/210) * 12) = (6, 12, -49)

Extended-Euclid(210, 858 MOD 210) -> Extended-Euclid(210, 18) -> (6, -1, 1 - floor(210/18) * -1) = (6, -1, 12)

Extended-Euclid(18, 210 MOD 18) -> Extended-Euclid(18, 12) - > (6, 1, 0 - floor(18/12) * 1) = (6, 1, -1)

Extended-Euclid(12, 18 MOD 12) -> Extended-Euclid(12, 6) -> (6, 0, 1 - floor(12/6) * 0) = (6,0,1)

Extended-Euclid(6, 12 MOD 6) -> Extended-Euclid(6, 0) b = 0

Return (6, 1, 0)

Final answer: (6, -49, 12)

Extended-Euclid(210,858) - > (6, -49, 12 - floor(210/858) * -49) = (6, -49, 12) Extended-Euclid(858, 210 MOD 858) -> Extended-Euclid(858, 210) - > (6, 12, -1 - floor(858/210) * 12) = (6, 12, -49) Extended-Euclid(210, 858 MOD 210) -> Extended-Euclid(210, 18) -> (6, -1, 1 - floor(210/18) * -1) = (6, -1, 12) Extended-Euclid(18, 210 MOD 18) -> Extended-Euclid(18, 12) - > (6, 1, 0 - floor(18/12) * 1) = (6, 1, -1) Extended-Euclid(12, 18 MOD 12) -> Extended-Euclid(12, 6) -> (6, 0, 1 - floor(12/6) * 0) = (6,0,1) Extended-Euclid(6, 12 MOD 6) -> Extended-Euclid(6, 0) b = 0 Return (6, 1, 0) Final answer: (6, -49, 12)

-- Mar 20 In-Class Exercise Thread

Extended-Euclid (210,858)	Return (6,-49,12)
Extended-Euclid (858,210)	Return (6,12,-49)
Extended-Euclid (210,18)	Return (6,-1,12)
Extended-Euclid (18,12)	Return (6,1,-1)
Extended-Euclid (12,6)	Return (6,0,1)
Extended-Euclid (6, 0)	Return (6,1,0)

(Edited: 2019-03-25)

{| |- | Extended-Euclid (210,858) || '''Return (6,-49,12)''' |- | Extended-Euclid (858,210) || Return (6,12,-49) |- | Extended-Euclid (210,18) || Return (6,-1,12) |- | Extended-Euclid (18,12) || Return (6,1,-1) |- | Extended-Euclid (12,6) || Return (6,0,1) |- | Extended-Euclid (6, 0) || Return (6,1,0) |}

-- Mar 20 In-Class Exercise Thread

With EE (a,b ) formula, we have EE( 210, 858) -->
EE ( 858, 210)-->
EE ( 210, 18)-->
EE (18, 12)-->
EE (12, 6)-->
EE (6,0)

EE(6,0) returns (6, 1, 0)
and with floor(12/6) = 2, EE (12,6) returns (6, 0, 1);
with floor(18/12) = 1, EE (18,12) returns (6, 1, -1);
with floor(210/18) = 11, EE (210, 18) returns (6, -1, 12);
with floor(858/210) = 4, EE (858,210) returns (6, 12, -49), returns (6, 12, -49).
Then EE(210, 858) returns final answer (6, -49, 12+49*0) = (6, -49, 12).

(Edited: 2019-05-15)

With EE (a,b ) formula, we have EE( 210, 858) --> EE ( 858, 210)--> EE ( 210, 18)--> EE (18, 12)--> EE (12, 6)--> EE (6,0) EE(6,0) returns (6, 1, 0) and with floor(12/6) = 2, EE (12,6) returns (6, 0, 1); with floor(18/12) = 1, EE (18,12) returns (6, 1, -1); with floor(210/18) = 11, EE (210, 18) returns (6, -1, 12); with floor(858/210) = 4, EE (858,210) returns (6, 12, -49), returns (6, 12, -49). Then EE(210, 858) returns final answer (6, -49, 12+49*0) = (6, -49, 12).