Question

2. Show that any positive odd integer is of the form 69+1, or 6q+3, or 69 +5, where q is
some integer.​

Answer 1

Answer:

lets us start with taking a,where a is a postive off integer

We apply the division algorithm with a and b=6

since 0 less than or equal to r or lessthan 6 the possible remainders are 012345

that is

a can be

6q+1or6q+3or6q+5

where quotient

however since a is odd a cannot be 6q,6q+2,6q+4since they are divisble by 2

therefore the any odd integer is of the form of 6q+1,6q+3,6q+5

Answer 2

for answer refer the picture above my friend