On the simultaneous equations $\sigma(2^a)=p^{f_1}q^{g_1}$, $\sigma(3^b)=p^{f_2}q^{g_2}$, $\sigma(5^c)=p^{f_3}q^{g_3}$
نویسندگان
چکیده
منابع مشابه
On the resolution of simultaneous Pell equations ∗
We descibe an alternative procedure for solving automatically simultaneous Pell equations with relatively small coefficients. The word “automatically” means to indicate that the algorithm can be implemented in Magma. Numerous famous examples are verified and a new theorem is proved by running simply the corresponding Magma procedure requires only the six coefficients of the system a1x 2 + b1y 2...
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15 صفحه اولSimultaneous Pell equations
Let R and S be positive integers with R < S. We shall call the simultaneous Diophantine equations x −Ry = 1, z − Sy = 1 simultaneous Pell equations in R and S. Each such pair has the trivial solution (1, 0, 1) but some pairs have nontrivial solutions too. For example, if R = 11 and S = 56, then (199, 60, 449) is a solution. Using theorems due to Baker, Davenport, and Waldschmidt, it is possible...
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It is proven that if a and b are distinct nonzero integers then the simultaneous Diophantine equations x − az = 1, y − bz = 1 possess at most three solutions in positive integers (x, y, z). Since there exist infinite families of pairs (a, b) for which the above equations have at least two solutions, this result is not too far from the truth. If, further, u and v are nonzero integers with av − b...
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ژورنال
عنوان ژورنال: Publicationes Mathematicae Debrecen
سال: 2018
ISSN: 0033-3883
DOI: 10.5486/pmd.2018.7992