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1
A Concrete Introduction to Higher Algebra
Hence the last nonzero remainder is a greatest common divisor of/ and g. From
Exercise E3, it follows that two greatest common divisors e and d off and g must
differ by a scalar multiple: d = ae for some a in F. For let d be the greatest
common ...
2
An Introduction to Mathematical Cryptography
We say that d is a greatest common divisor of a and b if every common divisor of
a and b also divides d. We will see below that every pair of elements in F[x] has a
greatest common divisor,10 which is unique up to multiplying it by a nonzero ...
Jeffrey Hoffstein, Jill Pipher, J.H. Silverman, 2008
3
Cassell's Arithmetic. The Elements of Arithmetic ... Edited ...
In a similar manner it may be shown that the last divisor will, in all cases, be the
greatest common divisor. I. To find the greatest common divisor of two numbers.
RULE—Divide the greater number by the less; then divide the preceding divisor ...
Robert WALLACE (A.M., Collegiate Tutor of the University of London.), 1852
4
Common Arithmetic: Upon the Analytic Method of Instruction. ...
We find that 15 will contain 5, therefore 5 is the greatest common divisor of 15
and 80. From this example, we perceive that the greatest common divisor of two
numbers, must be a common divisor of the least number and their remainder ofler
...
5
Arithmetic pure and commercial: for the use of schools
The greatest common divisor of the remainder and divisor is the greatest
common divisor of the dividend and divisor. Ex. Find the greatest common divisor
of 360 and 112. 360 H-112 gives remainder 24. 112 □— 24 gives remainder 16.
Charles Scott Venable, 1868
6
Common Arithmetic, upon the analytic method of instruction. ...
We find that 15 will contain 5, therefore 5 is the greatest common divisor of 15
and 80. .J From this example, we perceive that the greatest common divisor of
two'numbers, must be a common divisor of the least number and their remainder
afier ...
7
Encyclopaedia of Mathematics
AMS 1980 Subject Classification: 70F15, 83CXX, 83C35 Greatest common
divisor - The largest of the common divisors of a set of integers or, in particular, of
natural numbers a\, . . . ,a„. The greatest common divisor of a set of numbers not
all of ...
8
Morey's Practical Arithmetic ... Stereotype edition
Now I claim, that the greatest common divisor of the less and remainder, is the
greatest common divisor of the greater and less. For suppose the greater and
less have a common divisor, greater than the greatest common divisor of the less
and ...
9
Higher Arithmetic, Or, the Science and Application of ...
What is the greatest common divisor. of 532 and 1274 ? 10. What is the greatest
common divisor of-888 and 2775 '.7 11. VVhat is the greatest common divisor 7>f'
214,5 and 3471 '.7 12. What is the greatest common divisor of 1879 and-'2425 ...
James Bates Thomson, 1864
10
Common school arithmetic: combining the elements of the ...
Hence, 7, the greatest common divisor of itself and 14, is the greatest common
divisor of 21 and 77. PROEIEMS. 12. What is the greatest common divisor of 56
and 84 ? 28. 13. What is the greatest common divisor of .102 and .153 ? 51. 14.
ȘTIRI NOI CARE INCLUD TERMENUL «GREATEST COMMON DIVISOR»
Află ce ziare naționale și internaționale au scris despre și cum este întrebuințat termenul
greatest common divisor în contextul următoarelor știri.
Meet the heirs to Ramanujan's genius
One of these lectures explained the ancient Greek master Euclid's method to find the greatest common divisor of two numbers, involving two ... «Livemint, Iul 15»
Here's Why Splatoon Has Map-Rotation
I think if maps were selected at random from all the possibilities, everyone would only use weapons that have “the greatest common divisor” ... «Nintendo Enthusiast, Iun 15»
China Needs Critical Voices
... reach a consensus with all sectors of society, especially non-Party intellectuals and opinion leaders, and seek the greatest common divisor. «The Diplomat, Iun 15»
Big Vs, New Media, and China's 'United Front'
... promote democracy, respect and embrace differences and, as far as possible, carefully and patiently seek out the greatest common divisor.”. «The Diplomat, Iun 15»
Two security researchers break RSA 4096 bit keys with 'Phuctor'
The Phuctor tool, basically calculates the greatest common divisor (GCD) of two large numbers by using the euclidean algorithm method. «Techworm, Mai 15»
Microsoft vice president to cover history of computing at Cambridge …
Euclid's algorithm for the Greatest Common Divisor and continue through to PageRank, the 'billion dollar' algorithm that launched the search ... «Cambridge News, Oct 14»
French government vows deep attacks on the working class
Manuel Valls is the greatest common divisor of the left.” The major concern of Mélenchon and of the entire pseudo-left is that opposition in the ... «World Socialist Web Site, Apr 14»
Why Narendra Modi was declared BJP's PM candidate and what it …
... Common Factor (or, greatest common divisor) whose existence and value woefully depends on the numbers that constitute it. In BJP's history ... «NitiCentral, Sep 13»
The 'idea of Modi' is more critical than his acceptability
Singh resembled, in mathematical terms, the Highest Common Factor (or, the Greatest Common Divisor) which was created to blend with these ... «Firstpost, Iun 12»
Taking Sudoku Seriously
From here we have more theorems and proofs that make use of various simple properties of numbers such as the greatest common divisor function and modulo ... «iProgrammer, Mai 12»
