One of the quiz questions goes like this: If a is an odd integer, then the product of a, a−1, and a+1 is **always** divisible by how many integers from 1 to 9? The answer is 6 but can’t A be 1, and thereby making the product 0 overall?

That is a very specific case and not a general case. The question is asking for “always” which means for all odd integer values of a.

If a = 1, product = 0. Therefore, it is divisible by all integers.

If a = 3, product = 3×2×4. So, its divisible by only 1,2,3,4,6,8. Therefore, this eliminates other integers such as 5,7,9.

Now, we only need to find a case where we get a product which is not divisible by any of the above 6 integers to further eliminate potential divisors.

However, you will find no such case as the product is made up of numbers which when multiplied, is always divisible by all the 6 integers above.