True or False: If a|b and a|(b + 1), then a = ±1.

[NOTE: Use this Theorem 3: If a|b and a|c, then a|(bx+cy) for any integers x and y.
PROOF: Since a|b, there is an integer u such that b = au.
Since a|c, there is an integer v such that c = av.
Substituting, bx + cy = aux + avy = a(ux + vy)
since ux+ vy is an integer, a|(bx+cy). QED.]

I get stuck with my prove. I'm trying to following theorem 3.
Proof: Since a|b, there is integer u such that b=au
by theorem 3 tell us that a| b+1 - b. so we have a = ±1.

1. 👍
2. 👎
3. 👁
1. if a|b and a|c, then a|(b-c) (why?)
so,
if a|(b+1) and a|b,
a|(b+1-b)
a|1

1. 👍
2. 👎
2. thank you so much steve
i get it.
a|b, b=ae
a|b+1, b+1=af
substituting, ae+1=af
1=a(e-f), we conclude that a|b+1-b
therefore a|1, a = ±1

1. 👍
2. 👎

## Similar Questions

1. ### U.S. GOVERNMENT

1)Our federal bureaucracy takes care of the day-to-day business of our government. A) True B) False 2)There are 3 main elements of bureaucracy, which include a hierarchical structure with the president at the top, allowing for

2. ### Health JUST NEED ANSWERS CHECKED :)

1. The two health-related components of fitness are muscular strengthand muscular endurance. True False 2. Circuit resistance training utilizes only aerobic energy. True False 3. The training program for muscular endurance should

3. ### P.E

1. Air pollutants can do all of the following EXCEPT: A. damage the respiratory system. B. enter the bloodstream and harm other parts of the body. C. cause discoloration to your hair. D. reduce your protection from the sun's

4. ### Algebra 2 help :)

Any number in the form of a+-bi , where a and b are real numbers and b not equal 0 is considered a pure imaginary number. TRUE OR FALSE The minimum value is the smallest y-value of a function. T RUE OR FALSE i2 = square root of

1. ### Health

1. Your respiratory system is the system in your body that is responsible for breathing. True False 2. The lungs are made up of thick fibrous tissue. True False 3. Internal respiration takes place in the alveoli. True False 4. The

2. ### French Check Ms. Sue

Please check this. Thank you! 1. France is a country in Asia. true false*** 2. There are many countries in Africa where French is one of the principal languages of the people. true false 3. Québec, in Canada, is a French speaking

3. ### English

1. True or False: Shakespeare's works were written to be preformed on stage TRUE* FALSE 2. True or false: William Shakespeare married Anne Hathaway at the age of 30 in London True False* 3. Which of the following is NOT one of the

4. ### Career

QUESTION 1 -It is important to upgrade your skills as the career world is in a constant state of change. *True False QUESTION 2 -An important component of career planning is completing career research. *True False QUESTION 3 -When

1. ### math

Indicate whether each statement is true or false by checking the appropriate box in the table below. a. 2x is a factor of the expression (2x + y ). True or False b. (2x + y ) is a factor of the expression 3(2x + y ). True or False

2. ### Health

1. It is not possible to get a good workout at home. True *False 2. Most home equipment is expensive. *True False 3. A treadmill is a good choice of home equipment for a person who wants to improve their cardiovascular fitness.

3. ### health part2

The sole activity of the respiratory system is breathing. True False The exchange of gases between the blood and tissue cells is external respiration. True False Air flows in the process of pulmonary ventilation because of