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Question about modular equations

  1. Mar 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Solve each of the following sets of simultaneous congruences:
    {x=1(2),x=2(3),x=3(5),x=4(7)}
    {y=1(9),2(5),1(7)}
    3. The attempt at a solution
    I know how to solve the first one for x but on the second one
    with y im not sure what they mean
    so I have y=1mod9 and then 2mod5 should this be equal to y
    and same for 1mod7. if there not equal to y does that mean they have to be
    fixed at that value, for example 1mod7 would not equal 8 in his case.
    or does this mean that y=1mod9 is independent of 2mod5 and 1mod7
    so y would simply be 1
     
    Last edited: Mar 12, 2013
  2. jcsd
  3. Mar 12, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    You are supposed to find a y which satisfies all three equations at the same time. y=1 satisfies the first and third equation, but not the second one.

    I wonder how you solved the first one without that knowledge.
     
  4. Mar 12, 2013 #3
    because on the second one they just write the y one time.
    I didnt know if it meant something else.
     
  5. Mar 12, 2013 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, clearly they meant {y=1(9),y=2(5),y=1(7)}. No other interpretation is possible.
     
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