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Topic: Eulers totient function

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Leonhard Euler

Euler characteristic

Euler angles

Euler Mascheroni constant

Euler equations

Euler Lagrange equations

Euler numbers

Euler Maclaurin formula

Euler product

Euler Jacobi pseudoprime

Leonard Euler

Euler pseudoprime

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		A hash function or hash algorithm is a function for examining the input data and producing an output of a fixed length,...
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		In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomor...
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	[Leonhard Euler] \| [All the best Leonhard Euler resources at karaoke.velocityincome.com] (Site not responding. Last check: 2007-11-07)
		Euler was born in Basel to Paul Euler, a pastor of the Reformed Church, and Marguerite Brucker, a pastor's daughter.
		Leonhard Euler Eyesight deterioration Eyesight deterioration A 1753 portrait by Emanuel Handmann.
		Historia Mathematica 23 (2): 153-154. ^ Euler, Leonhard (1960).
	karaoke.velocityincome.com /Leonhard_Euler (4622 words)

	Leonhard Euler (Site not responding. Last check: 2007-11-07)
		Leonhard Euler was born on April 15, 1707 as the son of a Lutheran minister in Basel, Switzerland.
		Euler, with Daniel Bernoulli, established the law that the torque on a thin elastic beam is proportional to a measure of the elasticity of the material and the moment of inertia of a cross section, about an axis through the center of mass and perpendicular to the plane of the couple.
		Euler wrote Tentamen novae theoriae musicae in 1739 which was an attempt to combine mathematics and music; a biography comments that the work was "for musicians too advanced in its mathematics and for mathematicians too musical".
	leonhard-euler.ask.dyndns.dk (1310 words)

	Euler's totient function
		Euler's totient function φ(n), named after Leonhard Euler, is an important function in number theory.
		If n is a positive integer, then φ(n) is defined to be the number of positive integers less than or equal to n and coprime to n.
		The value of φ(n) is equal to the order of the group of units of the ring Z/nZ (see modular arithmetic).
	www.ebroadcast.com.au /lookup/encyclopedia/to/Totient.html (221 words)

	Euler's totient function (Site not responding. Last check: 2007-11-07)
		Euler's totient function φ(n) is defined for any positive integer n to be the number of positive less than or equal to n and coprime to n.
		Named after the Swiss mathematician Leonhard Euler φ(n) is an important function in number theory chiefly because it is the cardinality the multiplicative group of integers modulo n — more precisely the order of group of units of the ring Z / n Z (see modular arithmetic).
		The growth of φ(n) as a function of n is an interesting question since the impression from small n that φ(n) might be noticeably smaller than n is somewhat misleading.
	www.freeglossary.com /Eulers_phi_function (543 words)

	Euler's totient function at opensource encyclopedia (Site not responding. Last check: 2007-11-07)
		Euler's totient function φ(n) is defined, for any positive integer n, to be the number of positive integers less than or equal to n and coprime to n.
		Named after the Swiss mathematician Leonhard Euler, φ(n) is an important function in number theory, chiefly because it is the cardinality of the multiplicative group of integers modulo n — more precisely, the order of the group of units of the ring Z/nZ (see modular arithmetic).
		The growth of φ(n) as a function of n is an interesting question, since the first impression from small n that φ(n) might be noticeably smaller than n is somewhat misleading.
	wiki.tatet.com /Euler%27s_totient_function.html (420 words)

	Totient Function -- from MathWorld
		Since a number less than or equal to and relatively prime to a given number is called a totative, the totient function
		The totient function is implemented in Mathematica as
		The totient function is given by the Möbius transform of 1, 2, 3, 4,...
	www.m-brella.be /math/topics/TotientFunction.html (677 words)

	Definition of multiplicative function (Site not responding. Last check: 2007-11-07)
		'''multiplicative function''' is an [[arithmetic function]] ''f''(''n'') of the positive [[integer]] ''n''...
		is called an '''explicit function''', as it is a function being stated explicitly.
		functions are complementary to [[utilityutility functions]] which represent benefit and satisfaction.
	www.wordiq.com /search/multiplicative+function.html (951 words)

	NationMaster.com - Encyclopedia: 666 (number)
		There is no number whose value of Euler's totient function φ is 666, making it a nontotient.
		In number theory, the totient Ï†(n) of a positive integer n is defined to be the number of positive integers less or equal than n and coprime to n.
		A nontotient is a positive integer n which is not in the range of Eulers totient function φ, that is, for which φ(x) = n has no solution.
	www.nationmaster.com /encyclopedia/666-(number) (1907 words)

	Euler-Chelpin, Hans Karl August Simon von - Hutchinson encyclopedia article about Euler-Chelpin, Hans Karl August Simon ... (Site not responding. Last check: 2007-11-07)
		German biochemist who defined the structure of the yeast coenzyme, the nonprotein part of the yeast enzyme zymase that interlocks with the zymase and affects how it functions.
		He was awarded the Nobel Prize for Chemistry in 1929 for his work on the fermentation of sugar, and fermentative enzymes.
		Euler-Chelpin, who studied fermentation – a process that requires the presence of a yeast enzyme called zymase – showed that vitamins A and B activate zymase.
	encyclopedia.farlex.com /Euler-Chelpin,%20Hans%20Karl%20August%20Simon%20von (267 words)

	- d - » Blog Archive » Fun with the Euler phi function (Site not responding. Last check: 2007-11-07)
		Euler’s phi function for a number n determines how many numbers less than n are relatively prime to it.
		For such a “simple” function, it is quite interesting.
		We can first show that this function is even, for all n.
	aida.homelinux.net /wordpress/2005/02/fun-with-eulers-phi-function (311 words)

	Euler's theorem - TheBestLinks.com - Coprime, Integer, Leonhard Euler, Group (mathematics), ...
		Euler's theorem, Coprime, Integer, Leonhard Euler, Group (mathematics), Modular...
		In number theory, Euler's theorem (also known as the Fermat-Euler theorem) states that if n is a positive integer and a is relatively prime to n, then
		Using modern terminology, one may prove the theorem as follows: the numbers a which are relatively prime to n form a group under multiplication mod n, the group of units of the ring Z/nZ.
	www.thebestlinks.com /Euler__27__s_theorem.html (259 words)

	Euler's totient function: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-11-07)
		The totient function is also called Euler's phi function or simply the phi function, Exception Handler: No article summary found.
		The totient function is important mainly because it gives the size of the multiplicative group ((chemistry) two or more atoms bound together as a single unit and forming part of a molecule)
		Nontotient (A nontotient is a positive integer n which is not in the range of eulers totient function φ, that is,...)
	www.absoluteastronomy.com /ref/eulers_totient_function (1876 words)

	Totient Function (Site not responding. Last check: 2007-11-07)
		Totient is a multiplicative function -- that means when a and b are coprime (i.e.
		The Sum of Totients of Divisors of n is n
		Proof of: For any integer n, the sum of the totient values of each of its divisors equals n.
	mcraeclan.com /mathhelp/BasicNumberCoprimesTotientFunction.htm (732 words)

	smURN - Euler's Totient Function (Site not responding. Last check: 2007-11-07)
		A prize winning java implementation of Euler's Totient Function φ(n) using the Multiple Polynomial Quadratic Sieve algorithm...
		This year the task was to implement Euler's Totient Function φ(n) which is the number of positive integers smaller n that are relatively prime to n.
		To calculate the totient function the prime factors of n are needed.
	www.smurn.org /index.php?option=com_content&task=view&id=26&Itemid=1 (271 words)

	Euler's theorem - All About All
		In number theory, Euler's theorem (also known as the Fermat-Euler theorem or Euler's totient theorem) states that if n is a positive integer and a is coprime to n, then
		where φ(n) is Euler's totient function and "mod" denotes the congruence relation.
		The theorem is a generalization of Fermat's little theorem, and is further generalized by Carmichael's theorem.
	www.answers-zone.com /article/Euler%27s_theorem (298 words)

	Euler's totient function (Site not responding. Last check: 2007-11-07)
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	www.freeglossary.com /Euler's_phi_function (543 words)

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		Since the phi function is mulitplicate to a degree (phi(a) * phi(b) = phi(ab) iff (a,b)=1), and since we have trivially that (p,q)=1, since phi(p)=p-1, phi(q)=q-1, phi(pq)=(q-1)(p-1).
		The euler totient of this number phi(1487393335927) = 1487390891800.
		To find out how this number is calculated, search "euler's totient" or "phi euler" in google).
	www.antionline.org /archive/index.php/t-246625.html (2025 words)

	Euler Totient Function (Site not responding. Last check: 2007-11-07)
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