Problem
NT-B1-M01-P008 Transitivity of Divisibility
#8
★★☆☆☆ Level 2 of 5
Let \(a,b,c\) be positive integers. Prove: if \(a\mid b\) and \(b\mid c\), then \(a\mid c\).
Write \(b=ak\) and \(c=bm\).
From \(a\mid b\), we have \(b=ak\), and from \(b\mid c\), we have \(c=bm\), where \(k,m\) are integers. Then \(c=(ak)m=a(km)\). Since \(km\) is an integer, \(a\mid c\).
A good problem for precise use of the definition.