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A positive ineteger is of the form 3q+1, being a natural number. Can yoy write its square in any form other than 3m+1, 3m, 3m+2, for some integer m?

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Let a be any positive integer b=3                                                                    3q+1 where (qEN) a=3q+r where q>0                                                            r=0,1,2 because 0<r<3. therefore 3q+1                                                         (or)a²=(3q+1)²        ((a+b)²=a²+b²+2ab)                                                          (3q+1)²=(3q)²+(1)²+2(3q)(1)                                                                                     = 9q²+6q+1                                                                                                     =3(3q²+2q)+1             therefore where (3q²+2q)=m                                         =3m+1.
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it is correct because i wrote his answer 
what is his answer
no that is not his that is this answer ok
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