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299
An extension of Lucas’ theorem
 Proc. Amer. Math. Soc
"... Abstract. Let p be a prime. A famous theorem of Lucas states that ( mp+s) ≡ ( np+t m) ( s) (mod p) ifm, n, s, t are nonnegative integers with s, t < p. Inthispaper n t we aim to prove a similar result for generalized binomial coefficients defined in terms of second order recurrent sequences with ..."
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Cited by 26 (16 self)
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Abstract. Let p be a prime. A famous theorem of Lucas states that ( mp+s) ≡ ( np+t m) ( s) (mod p) ifm, n, s, t are nonnegative integers with s, t < p. Inthispaper n t we aim to prove a similar result for generalized binomial coefficients defined in terms of second order recurrent sequences
Optimal Taxation without StateContingent Debt
, 1996
"... To recover a version of Barro's (1979) `random walk' tax smoothing outcome, we modify Lucas and Stokey's (1983) economy to permit only riskfree debt. This imparts near unit root like behavior to government debt, independently of the government expenditure process, a realistic outcome ..."
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Cited by 201 (20 self)
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To recover a version of Barro's (1979) `random walk' tax smoothing outcome, we modify Lucas and Stokey's (1983) economy to permit only riskfree debt. This imparts near unit root like behavior to government debt, independently of the government expenditure process, a realistic
THE LUCAS TRIANGLE REVISITED
, 2002
"... The Lucas triangle is an infinite triangular array of natural numbers that is a variant of Pascal’s triangle. In this note, we prove a property of the Lucas triangle that has been merely stated by prior researchers; we also present some apparently new properties of the ..."
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The Lucas triangle is an infinite triangular array of natural numbers that is a variant of Pascal’s triangle. In this note, we prove a property of the Lucas triangle that has been merely stated by prior researchers; we also present some apparently new properties of the
Lucas Economy with Trading Constraints
, 2009
"... We are interested in a general equilibrium economy under leverage constraints. In the classical representativeagent Lucas economy, there is a unique stock price derived from the unique stateprice density. In our economy, agents have diverse beliefs about future performance so (following Brown and ..."
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Cited by 1 (0 self)
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We are interested in a general equilibrium economy under leverage constraints. In the classical representativeagent Lucas economy, there is a unique stock price derived from the unique stateprice density. In our economy, agents have diverse beliefs about future performance so (following Brown
A contraction of the Lucas polygon
 Proc. Amer. Math. Soc
, 2004
"... Abstract. The celebrated GaussLucas theorem states that all the roots of the derivative of a complex nonconstant polynomial p lie in the convex hull of the roots of p, called the Lucas polygon of p. We improve the GaussLucas theorem by proving that all the nontrivial roots of p0 lie in a smaller ..."
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Cited by 2 (0 self)
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Abstract. The celebrated GaussLucas theorem states that all the roots of the derivative of a complex nonconstant polynomial p lie in the convex hull of the roots of p, called the Lucas polygon of p. We improve the GaussLucas theorem by proving that all the nontrivial roots of p0 lie in a smaller
DIVISIBILITY BY FIBONACCI AND LUCAS SQUARES
"... In Matijasevic's paper [1] on Hilbert's Tenth Problem, Lemma 17 states that F 2 m divides Fmr if and only if Fm divides r. Here, we extend Lemma 17 to its counterpart in Lucas numbers and generalized Fibonacci numbers and explore divisibility by higher powers. In [2], Matijasevic's Le ..."
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In Matijasevic's paper [1] on Hilbert's Tenth Problem, Lemma 17 states that F 2 m divides Fmr if and only if Fm divides r. Here, we extend Lemma 17 to its counterpart in Lucas numbers and generalized Fibonacci numbers and explore divisibility by higher powers. In [2], Matijasevic
Note on the Lucas–Lehmer Test
 IRISH MATH. SOC. BULLETIN 54 (2004), 63–72
, 2004
"... A proof of the Lucas–Lehmer test can be difficult to find, for most textbooks that state the result do not prove it. Over the past two decades, there have been some efforts to produce elementary versions of this famous result. However, the two that we acknowledge in this note did so by using eithe ..."
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A proof of the Lucas–Lehmer test can be difficult to find, for most textbooks that state the result do not prove it. Over the past two decades, there have been some efforts to produce elementary versions of this famous result. However, the two that we acknowledge in this note did so by using
Extended LucasKanade Tracking
"... Abstract. The LucasKanade (LK) method is a classic tracking algorithm exploiting target structural constraints thorough template matching. Extended Lucas Kanade or ELK casts the original LK algorithm as a maximum likelihood optimization and then extends it by considering pixel object / background ..."
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Cited by 1 (0 self)
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Abstract. The LucasKanade (LK) method is a classic tracking algorithm exploiting target structural constraints thorough template matching. Extended Lucas Kanade or ELK casts the original LK algorithm as a maximum likelihood optimization and then extends it by considering pixel object
A Note on the Lucas Circles
"... Given a triangle ABC there is a similar triangle AB′C ′ such that B′C ′ is the side of an inscribed square. The circumscribed circle to AB′C ′ is a Lucas Circle. The Three Lucas Circles of a triangle are mutually tangent. This fact was proved in [1]. Here we give an alternative proof and we add some ..."
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− bc) , β = ca/(2b − ca) , γ = ab/(2c − ab) thus we have characterized the Lucas Circles of a triangle ABC by stating their radii. We proceed now to a geometric explanation. Let AD = h be the height from A in triangle ABC, then from the areaform we have bc = 2h, so we may write for the radius of OA, α
A Refinement Of The GaussLucas Theorem
"... The classical Gauss  Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull \Xi of the zeros of p. It is proved that, actually, a subdomain of \Xi contains the critical points of p. 1. ..."
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Cited by 8 (0 self)
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The classical Gauss  Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull \Xi of the zeros of p. It is proved that, actually, a subdomain of \Xi contains the critical points of p. 1.
Results 1  10
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299