Question 1
In Diophantine equations, what is structural reasoning mainly used to do?
Question 2
Why does $2x+4y=7$ have no integer solutions?
Question 3
What condition must hold if the linear Diophantine equation $ax+by=c$ has an integer solution?
Question 4
Which structural reason shows that $5x+10y=12$ has no integer solutions?
Question 5
Why can $x^2+y^2=3$ have no integer solutions?
