We also discussed the use of the Extended Euclidian algorithm
to calculate modular inverses. Use this algorithm to compute the
following values. Show all of the steps involved.
9570-1(mod 12935)
550-1 (mod 1769)
*NUMBER THEORY*
1.Find all the possible solutions for the following diphantine
equations by using the euclidian algorithim. You must show all the
process to get credit.
a.
3x + 5y = 7
b.
3x − 12y = 7
c.
1990x − 173y = 11
d.
21x + 48y = 6
e.
2x + 3y + 5z = 11
Sample Execution : ** Recursive Euclidean Algorithm to
calculate GCD **
Type a positive integer for A: -2
Sorry, you must enter a positive integer (>0). Please
try again.
** Recursive Euclidean Algorithm to calculate GCD **
Type a positive integer for A: 35
Type a positive integer for B: 63
The GCD is 7
Write a MIPS assembly program that prompts the user for 2
positive integers (>0). Then it uses the Recursive Euclidean
Algorithm to calculate GCD (the...
a. Using the Euclidean Algorithm and Extended Euclidean
Algorithm, show that gcd(99; 5) = 1 and find integers s1 and t1
such that 5s1 + 99t1 = 1.
[Hint: You should find that 5(20) + 99(?1) = 1]
b. Solve the congruence 5x 17 (mod 99)
c. Using the Chinese Remainder Theorem, solve the congruence
x 3 (mod 5)
x 42 (mod 99)
d. Using the Chinese Remainder Theorem, solve the congruence
x 3 (mod 5)
x 6 (mod 9)...
Write an algorithm to input a number n, then calculate 13 +2 3 +
33 + ... + n3, the sum
of the first n cubic numbers, and output the result.
2-Construct a trace table of the algorithm in question 1 with
input n=4.
find a linear combination for gcd(259,313). use
extended euclidean algorithm.
what is inverse of 259 in z subscript 313?
what is inverse of 313 in z subscript 259?
All necessary steps much show for these problems, please.
Use the Euclidean algorithm to find gcd(12345, 54321).
Write gcd(2420, 70) as a linear combination of 2420 and 70. The
work to obtain the gcd is provided.
2420 = 34(70) + 40
70 = 1(40) + 30
40 = 1(30) + 10
30 = 3(10) + 0
Determine if 1177 is prime or not. If it is not, then write
1177 as a product of primes
Find gcd(8370, 465) by unique...