Math
posted by Shay on .
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=66
6(216(3))=3
621+18=3
6( )21()=3
(216(3))(15)6=3 ???????

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