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Math Help - simple question that made me confused:(

  1. #1
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    simple question that made me confused:(

    how do i solve the simultaneous equation y is congruent to 6 mod 8 and y is congruent to 7 mod 10.

    if i tried to find the inverses of 8 and 10 and then use CRT, i got that y is congruent to 4 mod 80...

    but if i take that gcd(8,10) = 2 then 7 is not divisible by 2 so there is no solution..

    im not sure which is right..please help
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    how do i solve the simultaneous equation y is congruent to 6 mod 8 and y is congruent to 7 mod 10.

    if i tried to find the inverses of 8 and 10 and then use CRT, i got that y is congruent to 4 mod 80...

    but if i take that gcd(8,10) = 2 then 7 is not divisible by 2 so there is no solution..

    im not sure which is right..please help

    You want y\equiv 6\!\!\!\pmod 8\,,\,\,y\equiv 7\!\!\!\pmod{10} , right? Well, there's no solution since any number congruent to 7 modulo 10 is odd (why?), whereas any

    number congruent to 6 modulo 8 is even (why?)...

    Tonio
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  3. #3
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    so i cant use chinese remainder theormen by finding the inverse of 8 and 10 and then solving the simulataneous equation?


    becos using that 10= 1.8+2,

    i get that x= 6.10.1- 1.8.7 mod 80 = 4 mod 80
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  4. #4
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    Quote Originally Posted by alexandrabel90 View Post
    so i cant use chinese remainder theormen by finding the inverse of 8 and 10 and then solving the simulataneous equation?


    becos using that 10= 1.8+2,

    i get that x= 6.10.1- 1.8.7 mod 80 = 4 mod 80

    How can you use the CRT if 8, 10 are not coprime?!

    Tonio
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