MathDB

Let

n_1,\ldots,n_k

be positive integers, and define

d_1=1

and

d_i=\frac{(n_1,\ldots,n_{i-1})}{(n_1,\ldots,n_{i})}

, for

i\in \{2,\ldots,k\}

, where

(m_1,\ldots,m_{\ell})

denotes the greatest common divisor of the integers

m_1,\ldots,m_{\ell}

. Prove that the sums

\sum_{i=1}^k a_in_i

with

a_i\in\{1,\ldots,d_i\}

for

i\in\{1,\ldots,k\}

are mutually distinct

\mod n_1

Problem Statement