*If I turn out to have a wrong answer, please no hints or showing an valid proof. I want to do it on my own !
ad/bd-bc/bd=+-1/bd is neighbor fraction
Now, reduce the common numbers :
We must now prove that the left hand side has irreductible fractions. Lets see what would happen if these fraction were reductible.
let a=z*y , b=z*l , c=p*m d=p*n
z*y/z*l-p*m/p*n equality to be determined +-1/(z*l)*(p*n)
*ln (y/l-m/n) equality to be determined (+-1/(z*l)*(p*n))*ln
yn-lm equality to be determined +-1/z*p
yn-lm not= +-1/z*p
We have considered the initial fractions to be reductible and have arrived at a false result. An integer cannot be equal to (+-1/z*p)
So, the initial fractions must be irreductible.
*Of course, I'm considering the variables to represents integers.