Thales12345
New member
- Joined
- Jul 3, 2021
- Messages
- 30
A friend came up with the following question, but neither of us know the answer to it. Can someone help us?
GIVEN: a, b, c and d are natural numbers with a>b>c>d
ASKED: prove that (a-b)(a-c)(a-d)(b-c)(b-d)(c-d) is always a twelvefold
We are thinking of this method for now: perhaps it is possible to prove that the factors in (a-b)(a-c)(a-d)(b-c)(b-d)(c-d) are multiples of 2 and 3 (2*2*3 is the prime factorization of 12)?
GIVEN: a, b, c and d are natural numbers with a>b>c>d
ASKED: prove that (a-b)(a-c)(a-d)(b-c)(b-d)(c-d) is always a twelvefold
We are thinking of this method for now: perhaps it is possible to prove that the factors in (a-b)(a-c)(a-d)(b-c)(b-d)(c-d) are multiples of 2 and 3 (2*2*3 is the prime factorization of 12)?