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theorem proved term proof

bigOmega_prime_pow

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formal statement (Lean)

 499theorem bigOmega_prime_pow {p k : ℕ} (hp : Prime p) : bigOmega (p ^ k) = k := by

proof body

Term-mode proof.

 500  have hp' : Nat.Prime p := (prime_iff p).1 hp
 501  cases k with
 502  | zero => simp [bigOmega_apply]
 503  | succ k => exact ArithmeticFunction.cardFactors_apply_prime_pow hp'
 504
 505/-- ω(p^k) = 1 for prime p and k ≥ 1. -/

depends on (8)

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