Function extGcd

src/compute-engine/library/number-theory.ts:1153–1164

* Extended Euclidean algorithm: returns `[g, x, y]` with `a·x + b·y = g`, * where `g = gcd(a, b)` (its sign follows `a`/`b`; callers that need a * non-negative `g` normalize the triple).

(a: bigint, b: bigint)

          if (n === 0n && k === 0n) return 1n;
          if (n === 0n || k === 0n) return 0n;
          return S(n - 1n, k - 1n) + k * S(n - 1n, k);
        };
        return ce.number(S(nn, mm));
      },
    },

    StirlingS1: {
      description:
        'Signed Stirling number of the first kind s(n, m): the coefficient of x^m in the falling factorial x(x−1)…(x−n+1). Its absolute value counts the permutations of n elements with exactly m disjoint cycles.',
      signature: '(integer, integer) -> integer',
      type: () => 'finite_integer',
      examples: ['StirlingS1(5, 2)  // -50'],
      evaluate: ([n, m], { engine: ce }) => {
        const nn = toBigint(n);
        const mm = toBigint(m);