MathDB

Let

a

b

c

, and

d

be positive real numbers such that a^2 + b^2 - c^2 - d^2 = 0 \text{and} a^2 - b^2 - c^2 + d^2 = \frac{56}{53}(bc + ad). Let

M

be the maximum possible value of

\tfrac{ab+cd}{bc+ad}

. If

M

can be expressed as

\tfrac{m}{n}

, where

m

and

n

are relatively prime positive integers, find

100m + n

.
Proposed by Robin Park

Problem Statement