q — Mathlib · SciLib

English

For p ≠ 0, i arbitrary, sMod(p,i) is nonnegative as an integer.

Русский

Для p ≠ 0 и произвольного i, sMod(p,i) неотрицательно как целое.

LaTeX

$$0 \le sMod(p,i) \quad(\text{при } p \neq 0)$$

Lean4

/-- `q` is defined as the minimum factor of `mersenne p`, bundled as an `ℕ+`. -/
def q (p : ℕ) : ℕ+ :=
  ⟨Nat.minFac (mersenne p), Nat.minFac_pos (mersenne p)⟩
    -- It would be nice to define this as (ℤ/qℤ)[x] / (x^2 - 3),
    -- obtaining the ring structure for free,
    -- but that seems to be more trouble than it's worth;
    -- if it were easy to make the definition,
    -- cardinality calculations would be somewhat more involved, too.

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