Question

prove that out of any two consecutive positive integers one and only one in even is even

Answer 1

let two consecutive positive integers be x and y
then their product will be xy will also be even.
for xy to be even then one among them should be even.. eg.. 1,2 are consecutive numbers..product =2(which is even..inorder to be even it should contain one even number ..and here it is 2)and 1 is not even ..so in any two consecutive positive integers one and only one is even..take any other example 2,3 3,4 5,6 6,7 ..only one will be even