On The Generalized Ramanujan–Nagell Equation $$x^2+(2c-1)^m=c^n$$
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DOI: 10.1007/s10474-020-01085-8
Abstract: We show that if c is a positive integer satisfying $$2c-1=3p^l\ \hbox{or}\ 2c-1=5p^l$$ with p prime and l positive integer, then the equation $${x^2 + (2c-1)^m}=c^n$$ has only the positive integer solution $$(x,m,n)=(c-1,1,2)$$ without any… read more here.
Keywords: nagell equation; generalized ramanujan; ramanujan nagell; positive integer ... See more keywords
Convergence to Zero of Exponential Sums with Positive Integer Coefficients and Approximation by Sums of Shifts of a Single Function on the Line
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DOI: 10.1007/s10476-018-0204-2
Abstract: We prove that there is a sequence of trigonometric polynomials with positive integer coefficients, which converges to zero almost everywhere. We also prove that there is a function f: ℝ → ℝ such that the… read more here.
Keywords: convergence zero; sums shifts; integer coefficients; positive integer ... See more keywords
Complete solutions of the simultaneous Pell’s equations x2 − (a2 − 1)y2 = 1 and y2 − pz2 = 1
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DOI: 10.1142/s1793042119500593
Abstract: Let [Formula: see text] be a positive integer with [Formula: see text], and let [Formula: see text] be an odd prime. In this paper, by using certain properties of Pell’s equations and quartic diophantine equations… read more here.
Keywords: positive integer; text positive; formula see; see text ... See more keywords