If aN={an:n∈N}  and  bN∩cN=dN where a,b,c∈N and, b,c are coprime, then

Given that,aN={an:n∈N}bN={bn:n∈N} and cN={cn:n∈N}Also given,bN∩cN=dNbc∈bN∩cN or bc∈dNbc=d [∵b and c are coprime ][ coprime numbers are those numbers, whose common factor is 1. e.g., (i) 3 and 5 (ii) 5 and 9 etc.]