Question

show that any positive odd integer is of the form 6q+ 1 or 6q + 3 or 6q + 5 Where Q is positive integer

Answer 1

Hey

Here is your answer,

Let the positive odd integer be 'x'.

By Euclid's division lemma,

x=6q+r. (b=6)

So, 0 is equal to less than r .and r is less than 6.

So, R can have the values 0,1,2,3,4,&5.

So Putting values of r,

x = 6q+0. x=6q+4

x=6q+1, x=6q+3

x=6q+2 x=6q+5

But since, we have been given positive odd integer. Therefore, x≠6q, x≠6q+2 & x≠6q+4.

So, x(positive odd integer can be expressed in the form of 6q+1,6q+3 & 6q+5.

Hope it helps you!

Answer 2

Answer:

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