The pitch drop experiment is a long-term experiment that measures the flow of a piece of pitch over many years. Pitch is the name for any of a number of highly viscous liquids that appear solid, most commonly bitumen. At room temperature, tar pitch flows at a very low rate, taking several years to form a single drop.
== University of Queensland experiment ==
The best known version of the experiment was started in 1927 by Professor Thomas Parnell of the University of Queensland in Brisbane, Australia, to demonstrate to students that some substances that appear solid are, in fact, very-hig...
Note that you are wrong, as $13^2 \equiv -1 \not \equiv (-1)^2 \pmod {13}$. Note that $$13^{3} \equiv 13^2 \times 13 \equiv 169 \times 13 \equiv (-1) \times 13 \equiv -13 \equiv 21 \pmod {34}$$
Prove
$$\int_{-\infty}^{\infty}\frac{1}{(5 \pi^2 + 8 \pi x + 16x^2)
}\frac{\cosh\left(x+\frac{\pi}{4} \right)}{\cosh^3(x)}dx =
\frac{2}{\pi^3}\left(\pi \cosh\left(\frac{\pi}{4} \right)-4\sinh\left(
\frac{\pi}{4}\right) \right)$$
Attempt
Note that
$$\cosh\left( x+\frac{\pi}{4}\right)...
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