Let a denotes the number of non-negative P values of \( p \) for wh...

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Let a denotes the number of non-negative
P values of \( p \) for which the equation

W p. \( 2^{x}+2^{-x}=5 \) posses a unique solution.
If \( \frac{1}{a}, \frac{1}{\alpha_{1}}, \frac{1}{\alpha_{2}}, \ldots, \frac{1}{\alpha_{20}}, \frac{1}{6} \) are in \( \mathrm{AP} \) and \( a \), \( \beta_{1}, \beta_{2}, \ldots, \beta_{20}, 6 \) are in AP. Then, the number of digits in value of \( \alpha_{18} \beta_{3} \) is
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