We prove that if {un}n≥ 0 is a nondegenerate Lucas sequence, then there are only finitely many effectively computable positive integers n such |un|=f(m!), where f either the sum-of-divisors function, or sum-of-proper-divisors Euler phi function. also give theorem holds for more general class of integer sequences and illustrate our results through few specific examples. This paper motivated by p...

We count algebraic points of bounded height and degree on the graphs certain functions analytic unit disk, obtaining a bound which is polynomial in logarithm multiplicative height. combine this work with $p$-adic methods to obtain, for each positive $\varepsilon$, an upper form $cD^{3n/4 + \varepsilon n}$ number irreducible factors $P^{\circ n}(X)-P^{\circ n}(\alpha)$ over $K$, where $K$ field,...