- To see if a number, say 562437487, is divisible by 3, you just add up...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
- To see if a number, say 562437487, is divisible by 3, you just add up the digits of its decimal representation, and see if the result is divisible by 3. (5+ 6+2+4+3+7+4+8+ 7 = 46, so it is not divisible by 3.) To see if the same number is divisible by 11, you can do this: subdivide the number into pairs of digits, from the right-hand end (87, 74, 43, 62, 5), add these numbers, and see if the sum is divisible by 11 (if it's too big, repeat). How about 37? To see if the number is divisible by 37, subdivide it into triples from the end (487, 437, 562) add these up, and see if the sum is divisible by 37. This is true for any prime p other than 2 and 5. That is, for any prime p + 2,5, there is an integer r such that in order to see if p divides a decimal number n, we break n into r-tuples of decimal digits (starting from the right-hand end), add up these r-tuples, and check if the sum is divisible by p. (a) What is the smallest such r for p 13? For p = 17? (b) Show that r is a divisor of p-1. - To see if a number, say 562437487, is divisible by 3, you just add up the digits of its decimal representation, and see if the result is divisible by 3. (5+ 6+2+4+3+7+4+8+ 7 = 46, so it is not divisible by 3.) To see if the same number is divisible by 11, you can do this: subdivide the number into pairs of digits, from the right-hand end (87, 74, 43, 62, 5), add these numbers, and see if the sum is divisible by 11 (if it's too big, repeat). How about 37? To see if the number is divisible by 37, subdivide it into triples from the end (487, 437, 562) add these up, and see if the sum is divisible by 37. This is true for any prime p other than 2 and 5. That is, for any prime p + 2,5, there is an integer r such that in order to see if p divides a decimal number n, we break n into r-tuples of decimal digits (starting from the right-hand end), add up these r-tuples, and check if the sum is divisible by p. (a) What is the smallest such r for p 13? For p = 17? (b) Show that r is a divisor of p-1.
Expert Answer:
Answer rating: 100% (QA)
The statement above explains how to determine if a large number is divisible by certain primes by looking at its digits Specifically it describes proc... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these databases questions
-
Answer the following programming Questions. Use the information given below. (a) List and briefly describe other ways in which the syntax and the interpretation of query languages may vary. (b)...
-
123 Compare the purely graphical properties of these two notations, and the ways in which the graphical properties of each display correspond to the information structure being defined. Describe...
-
When researchers find a reasonably complete fossil of a dinosaur, they can determine the mass and weight of the living dinosaur with a scale model sculpted from plastic and based on the dimensions of...
-
Describe the type of information contained in a company's customer database and how that information is used.
-
Do size and value effects mean that small stocks outperform large stocks or value stocks outperform growth stocks in every year/every month? Explain.
-
How much noisier are streets where cars travel faster? The following table presents noise levels in decibels and average speed in kilometers per hour for a sample of roads. a. Compute the...
-
Prompt Parcel Service operates a fleet of delivery trucks in a large metropolitan area. A careful study by the companys cost analyst has determined that if a truck is driven 120,000 kilometres during...
-
18. (7 points) King Corp. uses 10,000 units of Part X in its production cycle. King can make or buy Part X. King's manufacturing costs for Part X are as follows: Per Unit Direct materials Direct...
-
Aaron, Deanne, and Keon formed the Blue Bell General Partnership at the beginning of the current year. Aaron and Deanne each contributed $110,000 and Keon transferred an acre of undeveloped land to...
-
The City of Moose Jaw borrowed $900,000 at 9% c.a. with interest to be paid yearly, the full principal due and payable in 9 years. A sinking fund is established with 9 annual payments to be made...
-
What are the gauge pressures at point A, B and C in each figure below? Water density is 1000 kg/m. The pressure po is the absolute pressure. Ambient pressure 101 325 Pa. Round off the answer to an...
-
AABC is right-angled at B, point D is the foot of the altitude from B to AC, and AB = AE. Prove that BE is the bisector of ZDBC.
-
With reference to Neil Patel, content marketing is a long-term strategy that focuses on building strong relationships with your target audience by consistently delivering high-quality, relevant...
-
Consider the 6 m long beam subjected to the loading shown. Ground reactions and the shear-force diagram are also presented. The maximum value of the positive moment M is most closely equal to 25 kN-m...
-
Microsoft has issued a 15-year bond, $1000 face value, paying semiannual coupons with a coupon rate of 9.5%. The yield to maturity on the bonds is 6.5%. If interest rates suddenly FALL by 2%, what is...
-
Using the table below, calculate 60 divided by 17 using the hardware described in Figure 3.8 (below). You should show the contents of each register on each step. Assume both inputs are unsigned 6-bit...
-
What do you think?
-
The following additional information is available for the Dr. Ivan and Irene Incisor family. The Incisors own a rental beach house in Hawaii. The beach house was rented for the full year during 2012...
-
Rebecca and Walter Bunge have been married for 5 years. They live at 883 Scrub Brush Street, Apt. 52B, Las Vegas, NV 89125. Rebecca is a homemaker and Walt is a high school teacher. Rebecca's Social...
-
William sold Section 1245 property for $25,000 in 2012. The property cost $35,000 when it was purchased 5 years ago. The depreciation claimed on the property was $16,000. a. Calculate the adjusted...
-
In an ideal gas mixture consisting of components \(A\) and \(B\), the partial pressure of component \(A\) is equal to (a) \(p_{\mathrm{A}}=\frac{n_{\mathrm{A}}-n_{\mathrm{B}}}{N}\) (b)...
-
The chemical potential of component \(i\) in a solution mixture can be expressed as (a) \(\mu_{i}=R T \ln G_{i}^{0}+a_{i}\) (c) \(\mu_{i}=R T \ln G_{i}^{0}-a_{i}\) (b) \(\mu_{i}=R T \ln...
-
For any pure substance, the difference between \(C_{P}\) and \(C_{V}\) can be expressed in terms of the isothermal compressibility \(\alpha\) and volume expansivity \(\beta\) as (a)...
Study smarter with the SolutionInn App