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The question is not rightly  formed.... It should be any odd positive integer.. Also  q should be a positive integer of 0.

any integer when divided by 4 gives a quotient q, and a reminder which is either 0, 1, or 2 or 3...  

so N = 4q    or  4 q +1  or  4 q+2  or  4 q+3      for a nonnegative integer q.
       4 q and  4 q + 2  are  even numbers. it is quite obvious.

  hence any odd positive integer is of the form  4q +1  or  4 q +3

equivalently also we can say  N is of the form:  4 q - 1  or  4q - 3

1 5 1