Theorems · Theorem · number theory
isPrimePow_iff_pow_succ
∀ {R : Type u_1} [inst : CommMonoidWithZero R] (n : R), IsPrimePow n ↔ ∃ p k, Prime p ∧ p ^ (k + 1) = nAn equivalent definition for prime powers: n is a prime power iff there is a prime p and a
natural k such that n can be written as p^(k+1).
- Defined in
- Mathlib.Algebra.IsPrimePow
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- CommMonoidWithZero
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Primestatement and proof · cited by 277
- IsPrimePowstatement · cited by 77
- Nat.succ_pos'proof · cited by 9
- isPrimePow_defproof · cited by 2
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