Question: Let m1, m2, . . . , mn be pairwise relatively prime integers greater than or equal to 2. Show that if a b

Let m1, m2, . . . , mn be pairwise relatively prime integers greater than or equal to 2. Show that if a ≡ b (mod mi) for i = 1, 2, . . . , n, then a ≡ b (mod m), where m = m1m2 · · ·mn. (This result will be used in Exercise 30 to prove the Chinese remainder theorem. Consequently, do not use the Chinese remainder theorem to prove it.)

Step by Step Solution

★★★★★

3.45 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We will argue for the truth of this statement using the Fundamental Theorem of Ari... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

923-M-C-M-S (1688).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Given n linear congruences modulo pairwise relatively prime moduli, find the simultaneous solution of these congruences modulo the product of these moduli.

Determine whether the integers in each of these sets are pairwise relatively prime. a) 11, 15, 19 b) 14, 15, 21 c) 12, 17, 31, 37 d) 7, 8, 9, 11

A rocket is fired straight up, burning fuel at the constant rate of kilograms per second. Let v = v(t) be the velocity of the rocket at time and suppose that the velocity of the exhaust gas is...

Use the Chinese remainder theorem to show that an integer a , with 0

Need answers with full explanation 00 (ilLet 3,- : Z aux\" . where the coefficients an are independent of x and are such that this series and all others in this n 2 0 00 question converge. Show that...

A common formulation of the Chinese remainder theorem (CRT) is as follows: Let $m_{1}, \ldots, m_{k}$ be integers that are pairwise relatively prime for $1 \leq i, j \leq k$, and $i eq j$....

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Explain informally the difference between Godel's completeness theorem and his first incompleteness theorem. [8 marks] (b) State the meaning of Hoare triples {P} C {Q} in separation logic. [3 marks]...

Consider Hoare triples of the form {T} V := E {V = E} where T is the atomic formula 'true' and V and E range over variables and expressions, respectively. (i) Write down an instance of such a triple...

In 2011, Derek Jeter hit a home run to become the twenty- eighth man to exceed 3,000 hits. This presented an interesting set of tax questions for the fan who caught the ball. In each case below, what...

SOLID is an acronym for the five object-oriented design (OOD) principles defined by Robert C. Martin. They are a set of rules and best practices to follow while desig ning a class structure. List and...

3. What purposes does the schedule of accounts receivable serve?

18. Consider the context of Exercise 17. (a) 9It is given that the marginal density of X is fX(x) = 12x 0 24x dy = 24x(1 2x), 0 x 0.5. Find fY|X=x(y) and the regression function E(Y|X = x). Plot...

Compute a 95% confidence interval for the population mean, based on the sample 10, 12, 13, 14, 15, 16, and 49. Change the number from 49 to 16 and recalculate the confidence interval. Using the...

The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the...

A large candy manufacturer is concerned that the mean weight of their bag of Gooey Sour Worms is not greater than 7.3 ounces. It can be assumed that the population standard deviation is .5 ounces...

please answer! The cost of debt Gronseth Drywall Systems, Inc., is in discussions with its investment bankers regarding the issuance of new bonds. The investment banker has informed to form that d...

What is the budgeted fixed operating expense for 20X4? (Use the following data to answer this question) Balance Sheet ASSETS Cash Account Receivable 12/31/20X3 100,000 250,000 250,000 100,000...

(Time allowance estimation: 7 minutes) You have won a swepstake that gives you 12 annual installments of $25,000 with the first one to be received one year from today. If the annual discounting rate...