frequently_even — Mathlib

English

For natural numbers n ≠ 0 and a residue d, there are infinitely many m with m ≡ d (mod n).

Русский

Для натуралов n ≠ 0 и остатка d существует бесконечно много m such that m ≡ d (mod n).

LaTeX

$$$\\forall n \\in \\mathbb{N}, n \\neq 0, \\forall d \\in \\mathbb{N},\\; \\exists^{\\infty} m \\in \\operatorname{atTop},\\; m \\equiv d \\pmod{n}$$$

Lean4

theorem frequently_even : ∃ᶠ m : ℕ in atTop, Even m := by simpa only [even_iff] using frequently_mod_eq zero_lt_two

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