Brushing up on my Algebra skills with the book "Algebra" by I.M. Gelfand and reached a problem I am unable to solve.
Fractions a/b and c/d are called neighboring fractions if their difference ad-bc/bd has numerator +-1, that is, ad-bc = +-1.
Fractions $a/b$ and $c/d$ are called neighboring fractions if their difference $\frac{ad-bc}{bd}$ has numerator $\pm1$, that is, $ad-bc = \pm1$.
Prove (a) In this case neither fraction can be simplified (that is, neither has any common factors in numerator or denominator).
Gelfand Algebra Neighboring fractions
What is a correct answer to this problem? Thank you.
