Math

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What are the 3 solutions? I'm stuck! 6x=15(mod 21)
a=6,m=21,b=15 d=gcd(6,21)=3 solns.
6x=15(mod 21) 2x=5(mod 7)
21=6(3)+3
6+3(2)+0
0=6-6
6-(21-6(3))=3
6-21+18=3
6( )-21()=3

(21-6(3))(15)-6=3 ???????

  • Math -

    6x = 21y + 15 for some y.
    or,

    2x = 7y + 5
    since 2x is even, y must be odd.

    y x
    1 6
    3 13
    5 20
    7 27
    . . .
    any number x of the form 2x = 7(2k+1)+5 is a solution, since

    2x = 14k+7+5 = 14k+12
    6x = 42k + 36
    and 36 = 15 mod 21

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