Question

Use Euclid division lemmato show that any positiveodd integer is of the form 6q+1,or
69 + 3 or 69 + 5, where is some integers.
that the same faryositive integer is of the form​

Answer 1

Let a be any integer and b =6 r=0 1,2,3,4,5

where q is some integer.

We know that,

sum of two odd numbers becomes even and sum of odd even becomes odd

summer of two even number becomes even itself

6q + 0 (r=0) even

6q + 1 (r=1) odd

6q + 2 (r=2) even

6q + 3 (r=3) odd

6q + 4(r=4) even

6q + 5 (r=5) odd

There fore, it is clear that any odd positive integer is of the form 6q + 1, 6q+3 , 6q + 5.