# Tag Info

18 Steps ...
• 3,401

### (-a) × (-a) = a × a

18 steps Different from the already posted 18-step solution. ...
• 390

### (-a) × (-a) = a × a

29 26 Steps No lemmas! Comment if you see anything wrong. (It's very easy to make a mistake) ...
• 11.6k

### How does the square end?

Google Sheets, 52 51 47 bytes =ArrayFormula(Join(",",Unique(Mod(Row(A:A)^2,A1 Saved 4 bytes thanks to Taylor Scott Sheets will automatically add 4 ...
• 9,439

### (-a) × (-a) = a × a

18 steps Not the first 18-step proof, but it’s simpler than the others. ...
• 39.7k
Accepted

### Demonstrate some advanced abstract algebra

Proof of impossibility The only anti-distributive operator when $S=\mathbb Z$ is such that $\forall a, \forall b, a*b=0$. Indeed, suppose that $*$ is anti-distributive. Then $*$ has the ...
• 15.6k

### Detect round trips on a hyperbolic grid

Python, 259 bytes ...
• 39.7k
Accepted

### Compute the inverse of an integer modulo 100000000003

Pyth, 24 bytes L-b*/bJ+3^T11Jy*uy^GT11Q Test suite This uses the fact that a^(p-2) mod p = a^-1 mod p. First, I manually reimplement modulus, for the specific ...
• 42k

### Fundamental Solution of the Pell Equation

Piet, 612 codels Takes n from standard input. Outputs y then x, space-separated. Codel size 1: Codel size 4, for easier viewing: Explanation Check out this NPiet trace, which shows the program ...
• 1,721

23 steps ...
• 393

### Multiply elements of the dihedral group

J, 23 bytes ~:/I.@,~4|[:-/1#;._1@,] Try it online! Takes a boolean vector where 0 represents ...
• 77k

### ∀ a b. a + b = b + a

Lean, 451 449 445 439 414 407 bytes ...

### Define a field with 256 elements

Python 2, 11 + 45 = 56 bytes Addition (11 bytes): int.__xor__ Multiplication (45 bytes): ...
• 61.9k

### ∀ a b. a + b = b + a

Lean, 268 bytes ...
• 39.7k

### Algebraic curve plotter

Haskell, 283 275 bytes The function g should be called with the matrix and the two ranges as arguments. The matrix is just a list of lists, the ranges each a two ...
• 43.8k

• 172k

### Compute the inverse of an integer modulo 100000000003

Haskell, 118 113 105 101 bytes Inspired from this solution. -12 from Ørjan Johansen ...
• 1,311
Accepted

### How does the square end?

Jelly, 5 bytes R²%³Q Try it online! Explanation ...
• 9,167

### Is the group cyclic?

Husk, 11 10 9 bytes VS≡`ȯU¡!1 1-based. Returns the index of a generator if one exists, 0 otherwise. Try it online! Explanation ...
• 42.7k

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### (-a) × (-a) = a × a

304 steps Community wiki because this proof is generated by Mathematica's FindEquationalProof function. The proof is rather long. Mathematica doesn't know how to golf it. This is the Mathematica ...

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