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On Smarandache least common multiple ratio
Smarandache LCM function and LCM ratio are already defined. This paper gives some additional properties and obtains interesting results regarding the figurate numbers. In addition, the various sequaences thus obtained are also discussed with graphs and their interpretations
The least common multiple of a quadratic sequence
For any irreducible quadratic polynomial f(x) in Z[x] we obtain the estimate
log l.c.m.(f(1),...,f(n))= n log n + Bn + o(n) where B is a constant depending
on f.Comment: 26 page
On the least common multiple of -binomial coefficients
In this paper, we prove the following identity \lcm({n\brack 0}_q,{n\brack
1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q},
where denotes the -binomial coefficient and
. This result is a -analogue of an identity of
Farhi [Amer. Math. Monthly, November (2009)].Comment: 5 page
Uniform lower bound for the least common multiple of a polynomial sequence
Let be a positive integer and be a polynomial with nonnegative
integer coefficients. We prove that except that and and that
with being an integer and , where denotes the
smallest integer which is not less than . This improves and extends the
lower bounds obtained by Nair in 1982, Farhi in 2007 and Oon in 2013.Comment: 6 pages. To appear in Comptes Rendus Mathematiqu
Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms
Let and be two integers with , and let and be
integers with and . In this paper, we prove that , where is a constant depending on and .Comment: 8 pages. To appear in Archiv der Mathemati
The least common multiple of a sequence of products of linear polynomials
Let be the product of several linear polynomials with integer
coefficients. In this paper, we obtain the estimate: as , where is a constant depending on
.Comment: To appear in Acta Mathematica Hungaric
Asymptotic behavior of the least common multiple of consecutive reducible quadratic progression terms
Let and be two integers with , and let be the
product of two linear polynomials with integer coefficients. In this paper, we
show that , where is a
constant depending only on , and .Comment: 13 page
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