query: Solution verification: a sloppy proof for 𝑑∣𝑛 ⟹ 𝜑(𝑑)∣𝜑(𝑛)
positive_passages.docid: 100515
positive_passages.text: Prove that if $d$ divides $n$ then $φ(d)$ divide $φ(n)$ for $φ$ denotes Euler’s φ-function.
negative_passages.docid: 153069
negative_passages.text: Proof for Unique Factorization Domain
negative_passages.docid: 61043
negative_passages.text: Proofs involving limsup and liminf
negative_passages.docid: 98372
negative_passages.text: Proof of the principle of backwards induction
negative_passages.docid: 46430
negative_passages.text: A simple decision problem whose decidability is not known
negative_passages.docid: 72391
negative_passages.text: linear dependence proof using subsets
negative_passages.docid: 85540
negative_passages.text: Prove or Disprove the Existence of Solutions...
negative_passages.docid: 133867
negative_passages.text: Security proofs for CBC mode
negative_passages.docid: 56528
negative_passages.text: On the proof of existence and uniqueness of radix representation
negative_passages.docid: 51465
negative_passages.text: New, elegant proofs for $\varphi(p^{k})=p^{k}-p^{k-1}$
negative_passages.docid: 27356
negative_passages.text: Lower bound on proof length
negative_passages.docid: 72371
negative_passages.text: Proof of Strong Induction Using Well-Ordering Principle
negative_passages.docid: 59885
negative_passages.text: Proof Verification - Every sequence in $\Bbb R$ contains a monotone sub-sequence
negative_passages.docid: 81879
negative_passages.text: $Av=λv$ basis proof problems
negative_passages.docid: 113305
negative_passages.text: Proof using Prüfer encoding
negative_passages.docid: 31340
negative_passages.text: Concurrent lines proof for a regular 18-gon
negative_passages.docid: 136694
negative_passages.text: Probabilistic Proof of Kraft-Mcmillan Inequality