Question

prove that every positive integer different from 1can be expressed as a product of a non - negative power of 2 and an odd numbers ?​

Answer 1

Answer:

If the given number n is odd, then n=1×n=(2^0)×n. If it is even, then it is divisible by 2. Let m be the largest positive integer such that 2^m divides n. ... Thus n can be uniquely written as a non-negative power of 2 multiplied by an odd integer.

Answer 2

Answer:

If we now write n as k. 2^m, then k has to be an odd integer because if k is even, then at least one power of 2 will divide k and so 2^(m+1) will divide n contradicting our choice of m as the highest power of 2 dividing n. Thus n can be uniquely written as a non-negative power of 2 multiplied by an odd integer