Question

Show that every postive even integer is of the form 2q and that every positive odd integer is of the form 2q+1 , where q is some integer.​

Answer 1

Answer:

Step-by-step explanation:

any positive integer n upon division by 2 yields either 0 or 1 as rest. if the rest is 0 then the integer is divisible by 2 and thus n = 2k, k positive integer. If the rest is 1 then n = 2k + 1 , k positive integer.

Answer 2

Answer:

Step-by-step explanation:

Let a be any positive integer and b=2 ..

Then by Euclid's division algorithm

a=2 q+r

For some integer q>or = to 0

And r =0 or r = 1 because 0 <r<2

So..

a= 2q +1

And a = 2q