Question

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

Answer 1

Let a be any +ve integer and b=6.then by EUCLID ALGORITHM a=6q+r,for some integer q>=0.

That is, a can be 6q or 6q+1 or 6q+2 or 6q+3 or 6q+4 or 6q+5,where q is quotient.
If a=6q or 6q+2 or 6q+4,then a is an even integdr. Also, an integer can be eben or odd. Therefore, any odd integer is of the form 6q+1 or 6q+3 or 6q+t,where q is some integer.

... Hope it will helpful for you...

Answer 2

HEY FRIEND HERE IS UR ANSWER,

Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5, because 0≤r<6.

Now substituting the value of r, we get,

If r = 0, then a = 6q

Similarly, for r= 1, 2, 3, 4 and 5, the value of a is 6q+1, 6q+2, 6q+3, 6q+4 and 6q+5, respectively.

If a = 6q, 6q+2, 6q+4, then a is an even number and divisible by 2. A positive integer can be either even or odd Therefore, any positive odd integer is of the form of 6q+1, 6q+3 and 6q+5, where q is some integer.

HOPE IT HELPS :)

MARK ME AS BRAINLIEST AND FOLLOW ME !!!!!!!!!!!!!!!!!!!!!