Question

Show that any positive even integer in the for m of4q or 4q+1, where q is an integer

Answer 1

hey !!
 here ,the pb goes like this....

let us start taking with a,where a is a positive odd integer. 
we apply euclids division algorithm with a and b=4.
  
    since 0≤r∠4 ,the possible remainders are 0,1,2,and 3....

that is , a can be 4q, or 4q+1 or 4q+2 , or 4q+3 ,where q is the quotient.
however, since a is odd , a cannot be 4q or 4q+2 (since they both r divisible by 2).
      ∴ any odd integer is a the form 4q+1 or 4q+3

hope my ans helps u.....^-^