Problem
NT-B1-M01-P002 Linear Combination
#2
★☆☆☆☆ Level 1 of 5
If \(5\mid a\) and \(5\mid b\), prove that \(5\mid 7a+4b\).
Set \(a=5x\), \(b=5y\).
Let \(a=5x\), \(b=5y\), where \(x,y\) are integers. Then \(7a+4b=35x+20y=5(7x+4y)\). Hence \(5\mid 7a+4b\).
It is important to state that \(7x+4y\) is an integer.