inequality

[penguin007]

Hi everyone,

1. The problem statement, all variables and given/known data

P(X)=Xp-1*(X-1)p*...*(X-n)p

j is an integer between 1 and n;
x a real beatween 0 and 1.

Prove that abs(P(jx))<=(n!)p
2. Relevant equations



3. The attempt at a solution

I tried to find an inequality for each abs(jx-q) but the problem is that I can't control j*x...


Any clue is welcome!

[Mark44]

Hi everyone,

1. The problem statement, all variables and given/known data

P(X)=Xp-1*(X-1)p*...*(X-n)p

j is an integer between 1 and n;
x a real beatween 0 and 1.

Prove that abs(P(jx))<=(n!)p
2. Relevant equations



3. The attempt at a solution

I tried to find an inequality for each abs(jx-q) but the problem is that I can't control j*x...


Any clue is welcome!

Please show us what you've tried. In particular, what do you have for P(jx)?

[penguin007]

Please show us what you've tried. In particular, what do you have for P(jx)?

For p(jx), you mean?:
P(jx)=(jx)p-1*(jx-1)p...(jx-n)p

I wanted to find an inequality for each abs((jx-q)), but my problem is that since jx is between 0 and n, I don't know the sign of jx-q...

I also tried:
* abs(jx-q)<=q, but this inequality is obviously wrong(for q=5, x=1 and j=11)...

*abs(P(jx))<=abs(P(j)) or abs(P(jx))<=abs(P(n*x)) so I could get rid of x or of j,but here too, these inequalities appears to be wrong...