Let a be a positive real number. Prove that a) There exists n∈N with φ(σ(n))σ(φ(n))>a.b) There exists n∈N with φ(σ(n))σ(φ(n))<a.(As usual, σ(n)=∑d∣nd and φ(n) is the number of integers 1≤m≤n which are coprime with n.)Proposed by Deniz Can Karaçelebi number theoryphi functionSigma function