- #1

Jonathanlikesmath

- 17

- 15

- Homework Statement
- The product of any five consecutive integers is divisible by 120.

- Relevant Equations
- N/A

This is more a general question that this problem spurred and this is what I came up with. I do not feel it is acceptable but would like clarification moving forward.

My text states the format for proof by contradiction is as follow;

Proposition: P

PF: Suppose ~P.

...a little math and logic...

Therefore C ^ ~C.

Proposition: The product of any five consecutive integers is divisible by 120.

PF: Suppose for sake of contradiction the product of any five consecutive integers is not divisible by 120.

If we pick the first five integers, 1,2,3,4,5 we have 5! = 120.

And 120 divides the product of five consecutive integers and we have a contradiction.

Q.E.D.

So, what I did was state P, then negate it and produce a contradiction from that negation. But it honestly feels "cheesy" and I am not sure it is allowed.

Thanks

Jonathan

My text states the format for proof by contradiction is as follow;

Proposition: P

PF: Suppose ~P.

...a little math and logic...

Therefore C ^ ~C.

Proposition: The product of any five consecutive integers is divisible by 120.

PF: Suppose for sake of contradiction the product of any five consecutive integers is not divisible by 120.

If we pick the first five integers, 1,2,3,4,5 we have 5! = 120.

And 120 divides the product of five consecutive integers and we have a contradiction.

Q.E.D.

So, what I did was state P, then negate it and produce a contradiction from that negation. But it honestly feels "cheesy" and I am not sure it is allowed.

Thanks

Jonathan