(1) Let a,b be coprime positive integers. Prove that there exists constants λ and β such that for all integers m, k=1∑m−1{mak}{mbk}−λm≤β (2) Prove that there exists N such that for all p>N (where p is a prime number), and any positive integers a,b,c positive integers satisfying p∤(a+b)(b+c)(c+a), there are at least ⌊12p⌋ solutions k∈{1,⋯,p−1} such that {pak}+{pbk}+{pck}≤1