Re: Congruence quesiton

On Sat, 16 Apr 2005 rammer202@xxxxxxxxx wrote:

> Solve the following congruences for x. Describe all solutions x to
> each of
> these congruences. If there is no solution, explain why.
> (a)
> 5x ( is congruent to ) 3 (mod 12)

5,12 coprime, thus some a,b with 5a + 12b = 1.
Use Euclidean algorithm to find a,b and adjust
by multiplicate factor from = 1 to = 3.

> (b)
> 12y ( is congruent to ) 1 (mod 72)

None, otherwise some a,b with 12a + 72b = 1.
But the smallest such for any a,b is 12a + 72b = (12,72) = 12

> (c)
> 111z ( is congruent to ) 11 (mod 226)
>
111 = 3*37; 226 = 2*113; 111 and 226 coprime.
Proceed as (a). As for finding all the solutions,
it's not my homework.
.