prove that for any integer n one and exactly one of the numb

prove that for any integer n one and exactly one of the numbers n and n+1 is even.

Solution

let both the integers n , n+1 are even or both odd

=>

(n+1) -n is also even (since difference of even numbers is even, difference of odd numbers is even)

=>

1 is even which is contradiction

=>

one and exactly one of the numbers n and n+1 is even

thus proved