Prove the following claims about divisibility. 1.The binary representation of any odd integer ends with a 1. 2. A positive integer n is divisible by 5 if and only if its last digit is 0 or 3.Let k be...

Prove the following claims about divisibility.

1.The binary representation of any odd integer ends with a 1.

2. A positive integer n is divisible by 5 if and only if its last digit is 0 or

3.Let k be any positive integer. Then any positive integer n is divisible by 2kif and only if its last kdigits are divisible by 2k. (This exercise is a generalization of Example 4.11.)