# simple question that made me confused:(

• Jun 1st 2010, 04:20 PM
alexandrabel90
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..

• Jun 1st 2010, 06:37 PM
tonio
Quote:

Originally Posted by alexandrabel90
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..

You want $\displaystyle y\equiv 6\!\!\!\pmod 8\,,\,\,y\equiv 7\!\!\!\pmod{10}$ , 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
• Jun 1st 2010, 07:36 PM
alexandrabel90
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
• Jun 1st 2010, 07:46 PM
tonio
Quote:

Originally Posted by alexandrabel90
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