Question

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

Answer 1

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.

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Answer 2

product of two odd positive integers is not disible by6

proof

let x and y be any two odd integers

xy is also  an odd integer

xy is  not divisible by 2

xy is  not divisible by  6