Determine whether each of these congruences has solutions. If so, find them...
a) x^2 congruent to 1 (mod 3)
b) x^2 congruent to 2 (mod 7)
c) x^2 congruent to 3 (mod 11)
a) I think it is just x=1 (mod 3) or x=2 (mod 3). Since x^2=1 and 1-1=0, which divides 3 and x^2=4 and 4-1=3, which divides 3. Is it that simple or am I doing things wrong?
b) So, this would be, by just checking them all: x=3(mod 7) or x=4 (mod 7)
c) x=2 (mod 11), x=5 (mod 11), x=6 (mod 11) is what I get.
Did I do these right?