The ABC conjecture and the powerful part of terms in binary recurring sequences. (English) Zbl 0923.11033

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 \(n\).


11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11D41 Higher degree equations; Fermat’s equation
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