The ABC conjecture and the powerful part of terms in binary recurring sequences (Q1284204)

Binary recurrence sequences have many interesting arithmetic properties like identities and divisibility properties. Under a certain assumption -- the so-called ABC conjecture is true -- such sequences with a positive discriminant have only finitely many terms which are powerful numbers. Here a natural number \(n\) is powerful if \(p^2\) divides \(n\) whenever a prime \(p\) divides \(n\).