Question

Very short Answer Questions
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your
answer.​

Answer 1

let us start with taking a , where a is a positive odd integer,. We apply the division algorithm with a and b =4.

since 0<r<4 , the possible remainders are 0,1,2,3.

that is , a can be 4q , or 4q+1, or 4q+2, or 4q+3, where q is quotient . however, since a is odd, a cannot be 4q or 4q+2.(since they are both divisible by 2)

therefore, any odd integer is of the form 4q+1 or 4q+3.