1 For each of the following pairs of numbers a and b, calculate and find integers...

Question

Question

Answer 1

Answer #1

203-91 x 2 2 21-7x3+O - . g.c d ( 203,91) = c. d ( 203 ,9 28l 3-2 2 8 32x) 3x 2

Answer 2

Similar Homework Help Questions

1. Let a, b,cE Z be positive integers. Prove or disprove each of the following (a)...

1. Let a, b,cE Z be positive integers. Prove or disprove each of the following (a) If b | c, then gcd(a, b) gcd(a, c). (b) If b c, then ged(a., b) < gcd(a, c)
PROBLEM 1 For each of the following pairs of integers, use the Euclidean Algorithm to find...

PROBLEM 1 For each of the following pairs of integers, use the Euclidean Algorithm to find ged(a,b), and to write gcd(a,b) as a linear combination of a and b, i.e. find integers m and n such that gcd(a,b) = am + bn. (a) a = 36, b = 60. (b) a = 12628, b = 21361. (c) a = 901, b = -935. (d) a = 72, b = 714. (e) a = -36, b = -60.
2. Let n be a positive integer. Denote the number of positive integers less than n and rela- tive...

number thoery just need 2 answered 2. Let n be a positive integer. Denote the number of positive integers less than n and rela- tively prime to n by p(n). Let a, b be positive integers such that ged(a,n) god(b,n)-1 Consider the set s, = {(a), (ba), (ba), ) (see Prollern 1). Let s-A]. Show that slp(n). 1. Let a, b, c, and n be positive integers such that gcd(a, n) = gcd(b, n) = gcd(c, n) = 1 If...

1. For each of the following pairs of numbers a and b, calculate ged(a,b) and find...

1. For each of the following pairs of numbers a and b, calculate ged(a,b) and find integers r and s such that ged(a,b) = ar +bs. (a) 14 and 39 (b) 234 and 164 Hint: Use the Euclid's Algorithm given in Example 2.12 in the textbook.
answer all parts please 1. (12 points) Prove that if n is an integer, then na...

answer all parts please 1. (12 points) Prove that if n is an integer, then na +n + 1 is odd. 2. (12 points) Prove that if a, b, c are integers, c divides a +b, and ged(a,b) -1, then god (ac) - 1. 3. (a) (6 points) Use the Euclidean Algorithm to find ged(270, 105). Be sure to show all the steps of the Euclidean algorithm and, once you have finished the Euclidean Algorithm, to finish the problem by...
2,3,4,5,6 please 2. Use the Euclidean algorithm to find the following: a gcd(100, 101) b. ged(2482,...

2,3,4,5,6 please 2. Use the Euclidean algorithm to find the following: a gcd(100, 101) b. ged(2482, 7633) 3. Prove that if a = bq+r, then ged(a, b) = ged(b,r). such that sa tb ged(a,b) for the following pairs 4. Use Bézout's theorem to find 8 and a. 33, 44 b. 101, 203 c. 10001, 13422 5. Prove by induction that if p is prime and plaja... An, then pla, for at least one Q. (Hint: use n = 2 as...

Question 2. Let a, b, c be natural numbers. (a) Suppose that g specific a, b,...

Question 2. Let a, b, c be natural numbers. (a) Suppose that g specific a, b, c eN where d > g. ged(a, b) ged(b, c). Let d ged(a, c); prove that d > g. Provide an example of (b) Let d gcd(a, b). By definition of the ged being a divisor of a, b, this implies that we may write a and b jd for some j,k E N. Prove that ged(j, k) = 1. kd -
This Question must be proven using mathematical induction 1: procedure GCD(a, b: positive integers) 2 if...

This Question must be proven using mathematical induction 1: procedure GCD(a, b: positive integers) 2 if a b then return a 3: 4: else if a b then 5: return GCD (a -b, b) 6: else return GCD(a,b-a) 8: end procedure Let P(a, b) be the statement: GCD(a, b)-ged(a,b). Prove that P(a, b) is true for all positive integer a and b.
Question 3 (a) Write down the prime factorization of 10!. (b) Find the number of positive...

Question 3 (a) Write down the prime factorization of 10!. (b) Find the number of positive integers n such that n|10! and gcd(n, 27.34.7) = 27.3.7. Justify your answer. Question 4 Let m, n E N. Prove that ged(m2, n2) = (gcd(m, n))2. Question 5 Let p and q be consecutive odd primes with p < q. Prove that (p + q) has at least three prime divisors (not necessarily distinct).

For number 25, can someone explain to me how they got (2^(ab-b)+2^(ab-2b)+2^(ab-3b)+...+(2^(ab-ab)) and how they reache...

For number 25, can someone explain to me how they got (2^(ab-b)+2^(ab-2b)+2^(ab-3b)+...+(2^(ab-ab)) and how they reached to that conclusion? For number 29, can someone explain to me how "it can't be greater than the greatest common divisor of a-b and b"? I would think that gcd(a, b) would be greater than gcd(a-b, b) because "a" and "b" are bigger than "a-b" and "b" so that confused me. Thank you! 25. Ifn e N and 2n - 1 is prime, then...