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

Answer:

let a be any positive odd integer and it is divided by 6

Step-by-step explanation:

a=bq+r

a=6q+r---------1

put r=0

a=6q

putr=1

a=6q+1

And now you put r=3,4,5

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.

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