Question

prove that any positive integer when squared is of the form 4m+1 where m is any positive no.

Answer 1

let 4m+1 be a positive no.
x=4q
squaring both sides 
x square =(4q)square
x square = (16q)square
              =  4(4q) square
              = 4m    ------------------- m is any integer
    squaring on both side
x square =(4q+1) square
               = (16q+1)square
              = 4(4q)+1
              = 4m+1 --------------------------m is any integer

                                                                          hence prove

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