Question:
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
This result is fell interesting, and This problem is from problem book, and this problem is name Siegel created it, and I searched sometimes and can't find it.and can't solve this problem, can someone help me?
Question:
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
This result is fell interesting, and This problem is from problem book, and this problem is name Siegel created it, and I searched sometimes and can't find it.and can't solve this problem, can someone help me?
Question:
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
This result is fell interesting, and This problem is from problem book, and this problem is name Siegel created it, and I searched sometimes and can't find it.and can't solve this problem, can someone help me?
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.Question:
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
This result is fell interesting, and This problem is from problem book, and this problem is name Siegel created it, and I searched sometimes and can't find it.and can't solve this problem, can someone help me?
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
This result is fell interesting, and This problem is from problem book, and this problem is name Siegel created it, and I searched sometimes and can't find it.and can't solve this problem, can someone help me?
Question:
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
This result is fell interesting, and This problem is from problem book, and this problem is name Siegel created it, and I searched sometimes and can't find it.and can't solve this problem, can someone help me?
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
This reslutresult is fell interesting,and and This problem is from problem book,and and this problem is name Siegel creatcreated it,and and I seachersearched sometimes and can't find it.and can't solve this problem,can you can someone help me?
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
This reslut is fell interesting,and This problem is from problem book,and this problem is name Siegel creat it,and I seacher sometimes and can't find it.and can't solve this problem,can you someone help me?
Let $$f(X)=(X-x_{1})(X-x_{2})\cdots (X-x_{n})$$ be an irreducible polynomial over the field of rational numbers,with integer coefficients and real zeros.
Prove that $$\prod_{1\le i<j\le n}|x_{i}-x_{j}|\ge\dfrac{n^n}{n!}$$
This result is fell interesting, and This problem is from problem book, and this problem is name Siegel created it, and I searched sometimes and can't find it.and can't solve this problem, can someone help me?
