MathDB

sum with residues, m is even and n is odd

Source: Romanian IMO TST 2005 - day 2, problem 2

April 1, 2005

calculusintegrationnumber theory proposednumber theory

Problem Statement

Let

m,n

be co-prime integers, such that

m

is even and

n

is odd. Prove that the following expression does not depend on the values of

m

and

n

\frac 1{2n} + \sum^{n-1}_{k=1} (-1)^{\left[ \frac{mk}n \right]} \left\{ \frac {mk}n \right\} .

Bogdan Enescu