Question

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

Answer 1

Answer:

The below is ur answer

Step-by-step explanation:

Let a be any positive integer and b = 6.

Then, by Euclid’s algorithm, a = 6q + r, where 0≤r<6 ,

r = 0, 1, 2, 3, 4, 5

If r = 0,

a = 6q + r

= 6q + 0

= 6q

= 2 * 3q

If r = 1,

a = 6q + 1

If r = 2,

a = 6q + 2

= 2 ( 3q + 1)

If r = 3,

a = 6q + 3

=3 ( 2q + 1 )

If r = 4,

a = 6q + 4

=2 (3q + 2)

If r = 5,

a = 6q + 5

2 is factor of all positive integers

6q , 6q + 2 , 6q + 4 are even numbers

Hence 6q + 1 , 6q + 3 and 6q + 5 are positive odd integers