MathDB

E (x, m) = \frac{sum [(2m -1)^ 4 + x + x]}{sum[(2m )^ 4 + x]}

Source: 2002 Moldova JBMO TST p5

February 25, 2021

algebra

Problem Statement

For any natural number

m \ge 1

and any real number

x \ge 0

we define expression

E (x, m) = \frac{(1^4 + x) (3^4 + x) (5^4 + x) ... [(2m -1)^ 4 + x]}{(2^4 + x) (4^4 + x) (6^4 + x) ... [(2m )^ 4 + x]}.

It is known that

E\left(\frac{1}{4},m\right)=\frac{1}{1013}.

. Determine the value of

m