Calculate gcd algorithm
[DOC File]Review Notes for Discrete Mathematics
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The Euclidean algorithm uses repeated division to determine the greatest common divisor of two integers a and b. At each step, the newly created remainder becomes the next number we use to divide. Here is an example of the algorithm with a = 135 and b = 47. Problem: Determine the GCD of 135 and 47 using the Euclidean Algorithm. 135 = 2x47 + 41
[DOC File]Information Technology course materials
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Using Euclidean algorithm calculate GCD (21,300) & GCD (125, 20) [K3 –Apply] (CO1) 4. Find GCD of (1403, 1081) [K3 –Apply] (CO1) 5. Explain Fermat’s little theorem and solve the following [K3 –Apply] (CO1) (i) 15 18 mod 17 (ii) 5 27 mod 13. 6. In a Chinese remainder theorem n=210, n1=5, n2=6 n3=7 and compute j -1 (3, 5, 2) i.e. given ...
[DOC File]Softspec: Software-based Speculative Parallelism
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One implementation of the intersect procedure solves the diophantine equation from section 2.3 exactly, by making use of Euclid’s algorithm to calculate gcd’s. Roughly 80-90% of the execution time for detecting parallelism was spent in the procedure that calculates the gcd.
[DOC File]Congruent Modulo n
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Then gcd (Ni, ni)=1. Hence there is a multiplicative inverse Ri (=Ni-1) of Ni (mod ni). Let X= . Since X= ai (mod ni), X is the unique solution. Example. If we line up the students in this class in 2 rows, there is one student left. If we line up them in 3 rows, there are two left. If we line up them in 5 rows, there are 3 left.
[DOC File]Ian Morrison - Cleveland State University
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The gcd(25,49) = 1. and is obvious by inspection. The solution to the equation is and . 1.(3) Find the solution set (if it exists), and compute one pair of integers that satisfies the equation . First, solve the equation . The gcd(385,84) = 7 from GCD algorithm in python. So let. 10 is not divisible by 7, so the equation has no integer ...
[DOC File]Lesson 1 : Introduction to Congruence and Modular Arithmetic
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The algorithm terminates when the remainder (calculated at each step) becomes zero. The previous remainder calculated is the greatest common divisor. Hence, gcd(274, 126) = 6. Example 5: Find the greatest common divisor of (a) 344 and 560, (b) 414 and 322. Observation 2:
[DOC File]Assignment # 3 : Solutions
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Section 3.8. 13. Use Euclidean algorithm to hand calculate gcd (544, 1001). Divide 1001 by 544 to get 1001 = 544 * 1+ 457. Hence gcd (1001, 544) = gcd (544, 457)
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