Question

Show that the square of an odd positive integer is of the form 6q+1 or 6q+3

Answer 1

Your answer is just below:)

Answer 2

Step-by-step explanation:

let a,b any two positive odd integer we apply the division algorithm with a and b =since ,0< r<6

the possible remainder are 0,1,2,3,4,5, it means a can be written

6q or 6a+1or6a +2 or ......

where a q is quotient

but since a odd . so a cannot be 6q ,6q+2,6q+4

hence any positive odd integer can be written in form 6q+1,6q+3,6q+5 .