Mathematics

Problem

Let

a_0, a_1, \dots, a_{23}

be real numbers such that

\left(1 + \frac{2}{5}x\right)^{23} = \sum_{i=0}^{23} a_i x^i

for every real number

x

. Let

a_r

be the largest among the numbers

a_j

for

0 \le j \le 23

. Then the value of

r

is ________.