Question

prove that product of two consecutive positive integer is divisible by two?

Answer 1

let us take two consecutive integer be x,x+2 and b=2
applying Euclid's division lemma,
a=bq+r
a=2q+r
0<=r<2
so..r=0 or 1
put the value of r =0
a=2q+r
a=2q+0
a=2q........(1)
put the value of r=1
a=2q+r
a=2q+1......(2)
product of two consecutive integers
(2q)(2q+1)
4q²+2q
2(2q²+q)
so here 2 is the factor hence, it is divisible by 2
so... now we can say that the product of two consecutive positive integers is divisible by 2