Monday, 20 October 2025

Exercise (1.3).6

Show that there is no integer solution to the linear equation $20x + 28y= 2$.


The smallest positive integer value of $20x + 28y$ is $\gcd(20,28)$, which is 4. 

Therefore the integer values of $20x + 28y$ cannot be 2, so the equation has no integer solutions.