1) Find the prime factorization of 111111.2) Find (-88 mod 13) 5 mod 7.3) Use the Euclidean algorithm to find gcd(144,233).

QUESTION #1 QUESTION #2 QUESTION #3

Answered: 1) Find the prime factorization of…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 34E

See similar textbooks

Similar questions

When we divide a polynomial P(x) by a divisor D(x), the Division Algorithm tells us that we can always obtain a quotient Q(x) and a remainder R(x). State two forms in which the result of this division can be written.
Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .
helpp
Pls help me
Find the smallest non negative value of D such that ED is congruent to 1 (mod b) when b=616 GCD=(5,616) use the extended Euclidean algorithm to find the value of D
1 Using prime factorization, find gcd(900, 140) and lcm(900, 140). 2. Use the Euclidean algorithm to determine gcd(900, 140) 3. Solve the linear congruence 31x ≡ 57 ( mod 61). 4. Express gcd(55, 17) as a linear combination of 55 and 17.
(7) Using the Euclidean algorithm find the multiplicative inverse of 253 mod 600 in Z600.
Fermat's Little Theorem tells us that if p is prime and a is an integer not divisible by p, then a-1=1(mod p) . Use this result to find the remainder when 13302 is divided by 31. Please note that both 13 and 31 are prime numbers.

Recommended textbooks for you

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

1) Find the prime factorization of 111111. 2) Find (-88 mod 13) 5 mod 7. 3) Use the Euclidean algorithm to find gcd(144,233).