Problem
NT-B2-M01-P003 A Linear Combination
#3
★★☆☆☆ Level 2 of 5
Prove that \(3n+2\) and \(5n+3\) are coprime for every integer \(n\).
Find a linear combination in which \(n\) disappears.
Any common divisor \(d\) of \(3n+2\) and \(5n+3\) divides \(5(3n+2)-3(5n+3)=1\). Hence \(d=1\), so the numbers are coprime.
Emphasise that the coefficients in the linear combination must be integers.