number theory

7^x≡1(mod 4)

find x(not necessary to be the smallest one).
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by my knowledge,

if a^x≡1(mod b) and a and b are relatively prime,then we can find x by euler function.
a^[ φ(b) ]≡1(mod b).

for detail,http://en.wikipedia.org/wiki/Euler's_totient_function

so in the above case,
x=φ(4) =2

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my question arise, if a and b is not relatively prime, how can i solve the question?