Abstract
Sury (2009) proved that the following two sets {(a1,…,ar)|ai∈[1,n],ai∈Z,gcd(a1,…,ar,n)=1}and {c|c∈[1,nr],c∈Z,pr∤gcd(c,nr),∀primep}have the same cardinality. And he asked whether there is a natural bijection between the above two sets. In this note, we will construct a natural correspondence between these two sets by p-adic expansion of integers and the Chinese remainder theorem.
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