Question

write whether every positive integers can be of the form 4q,4q+1,4q+2,4q+3

Answer 1

Hi
Every positive integer is if the form 4q, 4q+2

Answer 2

Let a be any positive integer and 
Let b be 4 then, according to Euclid's algorithm:
                    0 > or =  r  >  b
Then r can be 0,1,2,3,4
Also,we know that a = bq+r
Then a = 4q / 4q+1 / 4q+2/ 4q+3 / 4q+3 / 4q+4 (where q is some real no)
 
that is,
         any positive no is of the form 4q / 4q+1 / 4q+2 / 4q+3 / 4q+4
                               
                            Hence proved.