Show that an integer is divisible by 9 if and only if the sum of its decimal

Question:

Show that an integer is divisible by 9 if and only if the sum of its decimal digits is divisible by 9.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete Mathematics and Its Applications

ISBN: 978-0073383095

7th edition

Authors: Kenneth H. Rosen

See More Books

Question Posted: May 02, 2016 12:27 PM

See More Questions

Show that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3?
Show that a positive integer is divisible by 3 if and only if the difference of the sum of its binary digits in evennumbered positions and the sum of its binary digits in odd-numbered positions is...
Show that (k!)! is divisible by k!(k1)!.
For the following 28 scores on a 40-point test, a. Construct a bar graph using 4-point score intervals and b. Draw a frequency curve using 4-point score intervals. 27 24 21 36 25 25 38 27 25 17 31 20...
Suppose that you are the analyst charged with developing a new system to help senior managers make better strategic decisions. What requirements gathering techniques will you use? Describe in detail...
The following information relates to the Starr Companys Investment in Available-for-Sale Bonds account for 2007: Jan. 1 Purchased $30,000 face value of Bradford Company 8% bonds at 97 to yield 10%;...
Warmup Ltd produces outdoor gas fires for domestic use. The following information has been gathered so that a production budget, a direct materials budget and a direct labour budget for part of 2025...
Jake Corporation issued 1,000 shares of stock. Instructions Prepare the entry for the issuance under the following assumptions. (a) The stock had a par value of $5 per share and was issued for a...
Half a liter of gas in an air conditioner is initially at a temperature of 25 degrees Celsius and 2.0 atm of pressure. The volume of the gas is rapidly expanded to 2 L and the pressure of the gas...
Alice and Brendan exchanged the following business real estate: a. If Alice's adjusted basis in the undeveloped land was $360,000, compute Alice's realized gain, recognized gain, and basis in the...
Devise an algorithm for guessing a number between 1 and 2n 1 by successively guessing each bit in its binary expansion.
Prove there are infinitely many primes by showing that Qn = n! + 1 must have a prime factor greater than n whenever n is a positive integer.
Let k 1 = (k 1x , 0, k 1z ) be the wave vector of a plane wave incident on the x-y plane which separates simple medium 1 from simple medium 2. (a) Use (i) The Maxwell matching conditions for each...
On April 1, 2015, Pavlova Company received a condemnation award of $$410$,000 cash as compensation for the forced sale of the companys land and building, which stood in the path of a new highway....
Revenue is recognized for accounting purposes when a performance obligation is satisfied. In some situations, revenue is recognized over time as the fair values of assets and liabilities change. In...
On January 1, 2015, Barwood Corporation granted 5,000 options to executives. Each option entitles the holder to purchase one share of Barwoods 5 par value ordinary shares at 50 per share at any time...
On September 1, 2015, Tokachi Company sold at 104 (plus accrued interest) 30,000 of its 8%, 10-year, 10,000 face value, non-convertible bonds with detachable share warrants. Each bond carried two...
Capriati Corporation made the following cash investments during 2015, which is the first year in which Capriati invested in securities. 1. On January 15, purchased 9,000 ordinary shares of Gonzalez...
A survey conducted by CPA Australia shows that at least one in four small businesses are affected by fraud. Employee fraud was the most common type reported, with 10 per cent of small entities...
A statistical study shows that the fraction of television sets of a certain brand that are still in service after x years is given by f (x) = e-0.15x. (a) What fraction of the sets are still in...
Derive the expressions for the mean and variance of a geometric random variable with parameter p. (Formulas for infinite series are required.)
Suppose X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: (a) P(X = 1) (b) P(X =6) (c) P(X =4) (d) Determine the mean and variance of X.
Suppose X has a hypergeometric distribution with N = 20, n = 4, and K = 4. Determine the following: (a) P(X = 1) (b) P(X =4) (c) P(X =2 (d) Determine the mean and variance of X.
The following situation is an example for a fire detection and suppression system in an office building. The Initiating Event (IE) for the Event Tree is "fire starts", with a frequency of once every...
A one cubic foot sample of a borrow-source clay weighed 88 lbs. If the specific gravity of solids was measured as 2.70, and the clay was found to be 10 percent saturated, determine the water content...
Evaluate the use of novel catalytic systems, such as structured catalysts, catalytic distillation, and multifunctional catalysts, in achieving process intensification, discussing the effects on...

Show that an integer is divisible by 9 if and only if the sum of its decimal

Question:

Step by Step Answer:

Without loss of generality we may assume that the given in...View the full answer

Discrete Mathematics and Its Applications

Students also viewed these Statistics questions