Question

For some integer m , every odd integer is of from 2m+1

Answer 1

Let a be any positive integer and b=2

By Euclid's division Lemma, there exist integers m and r such that

a=2m+r, where 0≤r<2

Since 0≤r<2 => r=1 or r=2. [ ∵ r is an integer]

Thus, a=2m or a=2m+1

If a=2m, then a is an even integer.

we know that an Integer can be either even or odd.

Therefore, any odd integer is of the form 2m+ 1

Hence proved.