Posted by **Shay** on Thursday, August 2, 2012 at 11:32am.

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 -
**Steve**, Thursday, August 2, 2012 at 4:29pm
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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