Question

prove that the product of two consecutive positive integers is divisible by 6​

Answer 1

Answer:

it is not divisible because it must divisible by both 2 and 3 but it will only go through 2

Step-by-step explanation:

Let y and y + 1 are consecutive numbers.

Product of two consecutive numbers is y(y + 1)

If y is even number then

y = 2k and y+1 = 2k + 1

2k(2k + 1) is divisible by 2.

Similarly if y is odd number then y = 2k + 1 and y + 1 = 2k + 2

then y(y + 1) = (2k + 1)(2k + 2) = 4k2 + 6k + 2 = 2(2k2 + 3k + 1)

Which is also divisible by 2.

Hence, The product of two consecutive positive integers is not divisible by 6.