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Gaia, 5 bytes (this was produced by trying a bunch of languages from https://github.com/ETHproductions/golfing-langs until I found one that had the most useful built-ins for this problem) dụ⁇)u Expla …

Jelly, 5 bytes Ḷ²%ċ0 Uses the formula from the OEIS: the number of solutions to $$x^2 \equiv 0 \ (\mathrm{mod} \ n)$$ Explanation: implicit input range 0..n-1, square each modulo input (I got this p …

Pyt [sic!], 3 bytes Finally found the right language. I had a now-deleted answer in Vim, but it returned the empty string for an input of 1 :( 8+₀ Explanation: 8 In fact, I have no idea whethe …

Sledgehammer, 15 bytes so I just posted the winning answer to my own question ⡈⠀⣐⢕⠠⢵⠂⡒⡓⠄⠬⢔⣲⣔⢯ Take input as a list of two (or more) machine precision integers. Mathematica has all the built-ins you c …

disclaimer: the Mean mean is made up by me Define the arithmetic mean of \$n\$ numbers as $$M_1(x_1,...,x_n)=\frac{x_1+x_2+...+x_n}{n}$$ Define the geometric mean of \$n\$ numbers as $$M_0(x_1,...,x_n …

A wave of power \$k\$ is an infinite array that looks like \$1,2,\dots,k,k-1,\dots,1,\dots,k,\dots,1,\dots\$, and so on. For example, a wave of power 3 starts with \$1,2,3,2,1,2,3,2,1,...\$, and repea …

Sledgehammer, 17 bytes 16.75, to be overly specific ⣕⢌⢲⢼⠴⢺⢟⢼⣑⣮⣊⠞⠀⢄⡕⡝⢥ There's no point in trying to read that, so here's the corresponding Mathematica code with a reasonable explanation: ToExpression …

Wolfram Language (Mathematica), 20 bytes Mathematica has the inverse function of the factorial! It's called InverseFunction@Factorial. I used a pure (Mathematica for "anonymous") function that return …

Jelly, 12 bytes I wonder if this is the same as caird's answer (it probably isn't, because the control flow here almost certainly can be simplified by anyone who actually knows Jelly, or perhaps even …

C# (.NET Core), 62 38 bytes a=>c=>System.Numerics.Complex.Pow(a,c) Try it online!

Retina, 54 39 32 bytes This took really long to write (as I tried to golf it too) (unsurprisingly, all the golfing ideas only appeared after I finally posted this). Takes input as a list of strings o …

Wolfram Language (Mathematica), 11 bytes Mathematica has a built-in for pointing ion cannons. In fact, as far as I know, it should support self-intersecting roofs. Takes input as a polygon. RandomPo …

Wolfram Language (Mathematica), 25 bytes This uses a trick: Mathematica doesn't expand Sin[51819] into a proper number even when Max is called on a list of such things, and because of how Last works, …

Wolfram Language (Mathematica), 66 bytes Clearly the other Wolfram Language golfers only care about bytes. This program uses the beauty of Mathematica. GeoDistance@@Map[#~GeoPosition~Entity["Planeta …

Sledgehammer, 67 66 26 bytes -40 bytes thanks to @GregMartin and I also no longer have any idea about how my answer works Completes in less than a few seconds! ⡇⣄⠀⠇⣺⠇⢞⡞⣵⣍⠪⢺⡇⠜⢂⡒⢃⠦⠲⣎⠇⠣⡔⢻⡦⠔ Mathematica …