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2022-04-18
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-- Apr 13 In-Class Exercise Thread
a = 1 mod 2 a = 2 mod 3 a = 5 mod 7
m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6
EE(21,2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -10) EE(14,3) = EE(3, 2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) -> (1, -1, 5) EE(7,6) = EE(6, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1)
c1 = 21*1 = 21 c2 = 14*-1 = -14 c3 = 6*-1 = -6
a = 1*21 + 2*-14 + 5*-6 = -37 a = -37 mod 42 = 5 mod 42
It is clear that 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
a = 1 mod 2 a = 2 mod 3 a = 5 mod 7 m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6 EE(21,2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -10) EE(14,3) = EE(3, 2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) -> (1, -1, 5) EE(7,6) = EE(6, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) c1 = 21*1 = 21 c2 = 14*-1 = -14 c3 = 6*-1 = -6 a = 1*21 + 2*-14 + 5*-6 = -37 a = -37 mod 42 = 5 mod 42 It is clear that 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
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-- Apr 13 In-Class Exercise Thread
m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6
EE(21, 2) ->( call EE(2, 1) ->( call EE(1, 0) -> return (1, 1, 0) )-> return (1, 0, 1) ) -> return (1, 1, -10)
t1 = 1 mod 2
EE(14, 3) -> ( call EE(3, 2) ->( call EE(2, 1) ->( call EE(1, 0) -> return (1, 1, 0) )-> return (1, 0, 1) ) -> return (1, 1, -1) )-> return (1, -1, 5)
t2 = 1 mod 3
EE(6, 7) ->( call EE(7, 6) ->( call EE(6, 1) ->( call EE(1, 0) -> return (1, 1, 0) )-> return (1, 0, 1) )-> return (1, 1, -1) )-> return (1, -1, 2)
t3 = 1 mod 7
c1 = 21*1 = 21
c2 = 14*-1 = -14
c3 = 6*-1 = -6
a = 1 * 21 - 2 * 14 - 5 * 6 = 21 - 28 - 30 = -37 mod 42 = 5 mod 42
we can see that 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
(Edited: 2022-04-18)
m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6 EE(21, 2) ->( call EE(2, 1) ->( call EE(1, 0) -> return (1, 1, 0) )-> return (1, 0, 1) ) -> return (1, 1, -10) t1 = 1 mod 2 EE(14, 3) -> ( call EE(3, 2) ->( call EE(2, 1) ->( call EE(1, 0) -> return (1, 1, 0) )-> return (1, 0, 1) ) -> return (1, 1, -1) )-> return (1, -1, 5) t2 = 1 mod 3 EE(6, 7) ->( call EE(7, 6) ->( call EE(6, 1) ->( call EE(1, 0) -> return (1, 1, 0) )-> return (1, 0, 1) )-> return (1, 1, -1) )-> return (1, -1, 2) t3 = 1 mod 7 c1 = 21*1 = 21 c2 = 14*-1 = -14 c3 = 6*-1 = -6 a = 1 * 21 - 2 * 14 - 5 * 6 = 21 - 28 - 30 = -37 mod 42 = 5 mod 42 we can see that 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
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-- Apr 13 In-Class Exercise Thread
a = 1 mod 2 a = 2 mod 3 a = 5 mod 7
m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6
EE(21,2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -10) EE(14,3) = EE(3, 2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) -> (1, -1, 5) EE(7,6) = EE(6, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1)
c1 = 21*1 = 21 c2 = 14*-1 = -14 c3 = 6*-1 = -6
a = 1*21 + 2*-14 + 5*-6 = -37 a = -37 mod 42 = 5 mod 42
we have 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
a = 1 mod 2 a = 2 mod 3 a = 5 mod 7 m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6 EE(21,2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -10) EE(14,3) = EE(3, 2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) -> (1, -1, 5) EE(7,6) = EE(6, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) c1 = 21*1 = 21 c2 = 14*-1 = -14 c3 = 6*-1 = -6 a = 1*21 + 2*-14 + 5*-6 = -37 a = -37 mod 42 = 5 mod 42 we have 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
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-- Apr 13 In-Class Exercise Thread
a = 1 mod 2 a = 2 mod 3 a = 5 mod 7
m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6
EE(21,2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -10) EE(14,3) = EE(3, 2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) -> (1, -1, 5) EE(7,6) = EE(6, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1)
c1 = 21*1 = 21 c2 = 14*-1 = -14 c3 = 6*-1 = -6
a = 1*21 + 2*-14 + 5*-6 = -37 a = -37 mod 42 = 5 mod 42
we have 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
a = 1 mod 2 a = 2 mod 3 a = 5 mod 7 m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6 EE(21,2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -10) EE(14,3) = EE(3, 2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) -> (1, -1, 5) EE(7,6) = EE(6, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) c1 = 21*1 = 21 c2 = 14*-1 = -14 c3 = 6*-1 = -6 a = 1*21 + 2*-14 + 5*-6 = -37 a = -37 mod 42 = 5 mod 42 we have 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
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-- Apr 13 In-Class Exercise Thread
Resource Description for 20220418_162656.jpg
((resource:20220418_162656.jpg|Resource Description for 20220418_162656.jpg))
User Icon
-- Apr 13 In-Class Exercise Thread
a = 1 mod 2 a = 2 mod 3 a = 5 mod 7
m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6
EE(21,2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -10) EE(14,3) = EE(3, 2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) -> (1, -1, 5) EE(7,6) = EE(6, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1)
c1 = 21*1 = 21 c2 = 14*-1 = -14 c3 = 6*-1 = -6
a = 1*21 + 2*-14 + 5*-6 = -37 a = -37 mod 42 = 5 mod 42
we have 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
a = 1 mod 2 a = 2 mod 3 a = 5 mod 7 m1 = 42/2 = 21 m2 = 42/3 = 14 m3 = 42/7 = 6 EE(21,2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -10) EE(14,3) = EE(3, 2) = EE(2, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) -> (1, -1, 5) EE(7,6) = EE(6, 1) = EE(1, 0) -> (1, 1, 0) -> (1, 0, 1) -> (1, 1, -1) c1 = 21*1 = 21 c2 = 14*-1 = -14 c3 = 6*-1 = -6 a = 1*21 + 2*-14 + 5*-6 = -37 a = -37 mod 42 = 5 mod 42 we have 5 = 1 mod 2, 5 = 2 mod 3, 5 = 5 mod 7
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-- Apr 13 In-Class Exercise Thread
Resource Description for IMG_20220419_012959__01.jpg
(Edited: 2022-04-19)
((resource:IMG_20220419_012959__01.jpg|Resource Description for IMG_20220419_012959__01.jpg))
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