Diophantine Equations Involving Arithmetic Functions of Factorials
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چکیده
DIOPHANTINE EQUATIONS INVOLVING ARITHMETIC FUNCTIONS OF FACTORIALS Daniel M. Baczkowski We examine and classify the solutions to certain Diophantine equations involving factorials and some well known arithmetic functions. F. Luca has showed that there are finitely many solutions to the equation:
منابع مشابه
Equations Involving Arithmetic Functions of Factorials Ecuaciones que Involucran Funciones Aritméticas de Factoriales
For any positive integer k let φ(k), σ(k), and τ(k) be the Euler function of k, the divisor sum function of k, and the number of divisors of k, respectively. Let f be any of the functions φ, σ, or τ . In this note, we show that if a is any positive real number then the diophantine equation f(n!) = am! has only finitely many solutions (m,n). We also find all solutions of the above equation when ...
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