Question: Let x and y be integers such that 7 | (3x + 5y). Prove that 7 | (16x + 29y).

Let x and y be integers such that 7 | (3x + 5y). Prove that 7 | (16x + 29y).

Step by Step Solution

★★★★★

3.48 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

3x 5y 7k 16x 29y 112k 24k 136k Explanation We know that 7 divides 3x 5y We can write this as 7... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

Q:

Let X and Y be compact subsets of a finite-dimensional normed linear space, and let f be a continuous functional on X Ã Y. Then if and only if there exists a point (x*, y*) X Ã Y such...

Q:

Let X and Y be independent random variables with uniform densities in [0, 1]. Let Z = X + Y and W = X Y. Find (a) p (X, Y ) (see Exercise 18). (b) p (X,Z). (c) p (Y,W). (d) p (Z,W).

Q:

Let X and Y be independent random variables with uniform densities in [0, 1]. Let Z = X + Y and W = X Y. Find (a) p (X, Y ) (see Exercise 18). (b) p (X,Z). (c) p (Y,W). (d) p (Z,W).

Q:

7. Let a and b be integers such that a

Q:

Consider the numbers in Table 10.40 on page 676. Suppose that you have available as many standard normal random variables and as many uniform random variables on the interval [0, 1] as you desire....

Q:

Consider a sequence of independent flips of a biased coin. The coin is a Head or Tail with probabilities p or q : = 1 - p, respectively. Let X be the smallest j such that the jth and (j + l)st flips...

Q:

Let S be a nonempty, closed, convex set in a Euclidean space X and y S. There exists a continuous linear functional f X* and a number c such that f (y)

Q:

Let F and g be function such that 0 ¤ F(x) ¤ G(x) for all x near c, except possibly at c. Prove that if Then lim G(x)0, lim F(x) 0.

Q:

Let X be a random variable such that P(X = k) = k/10, for k = 1, 2, 3, 4. Let Y be a random variable with the same distribution as X. Suppose X and Y are independent. Find P(X + Y = k), for k = 2, ....

Q:

Let X be a random variable such that P(X 0) = 0 and let = E(X) exist. Show that P(X 2) 1/2.

Q:

The world of fast food, especially the world of hamburgers and fries, continues to evolve. The dominant force for nearly 40 years has been McDonald's. The company is an icon in the United States and...

Q:

RevHeads Ltd has a policy of adjusting the net book value of its non-current assets to fair value if the two values are significantly different. The only asset that required revaluing prior to 1 July...

Q:

Consider the following. 0 5 d t 2 5 + t 2 2 Let t = 5 t a n ( ) and determine the following. Evaluate the integral.

Q:

11) A statistics exam has meanu=78 and standard deviationG=10 ESTIMATE the portion of grades between 62 and 94. 12) Which of these could NOT be probabilities: a) 4/5 b) .45454545 c) 5/4 d) 54% e) 540%

Q:

10) Carmen and Jackie apply for the same job. Both took comparable aptitude tests. Carmen got 170 on the ABC test where x= 100 and s =40 Jackie got 660 on the XYZ test where x= 500 and s-100 Which of...

Q:

7) -4, 6, 37, 3. Find a)$(x-X) b)x )(x )*

Q:

9) The Stanford-Binet IQ exam has a mean of x = 100 and standard deviation s =15 What IQ has a z-score of -1.4

Q:

5) A,B,C and D are events: P(A) =.10, P(B) =.45 P(C) =..70 P(D) =..85. Which of these events are a) Most likely b) Least likely c) Most predictable d) Least predictable

Q:

When a man observed a sobriety checkpoint conducted by a police department, he saw 691 drivers were screened and 5 were arrested for driving while intoxicated. Based on those results, we can estimate...

Q:

Suppose that the number of minutes required to serve a customer at the checkout counter of a supermarket has an exponential distribution for which the mean is 3. Using the central limit theorem,...

Q:

Suppose that the probability of a head on any toss of a certain coin is p (0

Q:

Suppose that 20 percent of the students who took a certain test were from school A and that the arithmetic average of their scores on the test was 80. Suppose also that 30 percent of the students...

Q:

Motion sickness often results from conflicting signals sent from the _______________ and from the __________. a. eyes; vestibular organs b. extremities; brain c. brain; internal organs d. conscious;...

Q:

When opening a door, the actual image on your retina changes drastically, but you still perceive the door as a rectangle. This is an example of a. color constancy. b. size constancy. c. shape...

Q:

The Mller-Lyer illusion occurs more frequently in a. people living in a Western culture. b. children than adults. c. men than women. d. individuals living in poverty.