MathDB

Let n be an integer which is greater than 1, not divisible by 1997. Let a_m\equal{}m\plus{}\frac{mn}{1997} for all m=1,2,..,1996 b_m\equal{}m\plus{}\frac{1997m}{n} for all m=1,2,..,n-1 We arrange the terms of two sequence

(a_i), (b_j)

in the ascending order to form a new sequence c_1\le c_2\le ...\le c_{1995\plus{}n} Prove that c_{k\plus{}1}\minus{}c_k<2 for all k=1,2,...,1994+n

Problem Statement