Let A(x)= ∑_i=1^k n_if(x+m_i). The Semenov's conditions are:

1. f is strongly monotone
   
   
2. for any integer numbers n₁,…, n_k, m₁,…, m_k, there is natural δ such that either |A(x)|<δ for all natural x, or |A(x+δ)|>f(x) for all natural x
   
   
3. for any integer numbers n₁,…, n_k, m₁,…, m_k, either A(x)>0 for almost all natural x, or A(x)<0 for almost all natural x, or A(x)=0 for all x
   
   
4. f module m is periodical for all positive m
   
   Previous page
   Next page