Question: show that if a , b , c , and n are integers with n > = 2 , c > 0 and a b

show that if a, b, c, and n are integers with n >=2, c >0 and a b mod n, then ac bc mod nc.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock 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 Databases Questions!

Q:

1. Show that if a, b, c, and d are integers where a 0, such that a|c and b|d, then ab|cd. 2. Suppose that a and b are integers, a ? 11 (mod 19), and b ? 3 (mod 19). Find the integer c with 0 ? c ? 18...

Q:

2. (Number Theory - 20 pt.) a. (5 pts.) Show that if a, b, c, and m are integers with m 2 2,c> O and a = b (mod m) then ac = bc (mod mc) b. (15 pt.) A hashing function h assigns memory location h(k)...

Q:

discrete mathematics Show that if a, b, c and d are integers, where a notequalto 0, such that a|c and b|d then ab|cd. Prove or disprove that if a|bc, where a, b, and c are positive integers and a...

Q:

Show that (a) AB + AC = A(B + C); and (b) BA + CA = (B + C)A. [In general, if A is an m à n matrix and B, C are n à p matrices, then AB + AC = A(B + C). For n à p matrices B, C...

Q:

04. (2+3+ 3 =8 marks) Let P. (x) be the degree 04. (2 + 3 + 3 = 8 marks) Let Pn (x) be the degree equidistant points n polynomial that interpolates the function f (x) 1 4' e at the n Show that max a....

Q:

2/ 10 pts ] Show that 4x2 + 7x log (x)-1 is 0(*) . 3. [ 15 pts ] Suppose n >1 and m >1 are integers and n I m. Show for integers a and b that if a b (mod m), then a b (mod n) 4. [ 15 pts ] Show that...

Q:

Answer the following questions: a,b,c,d,e,f,g, and h. (a) For each of the following congruences, find the least non-negative integer r such that r = b (mod c). (i) r = 15 (mod 4) (ii) r = 23 (mod 3)...

Q:

Discsrete Math, I need a complete solution. 7. Number Theory[12.5pt]. Prove that if n E Z then n2 0 (mod 4) or n 1 (mod 4). 8. Number Theory[12.5pt]. Show that if a, b, c and m are integers such that...

Q:

Question 1 (2.5 points) Below is a proof of a result. Proof: Case 1: Assume a and b are even. Then a = Zr and b = 25 for integers r and 5. Thus aszrZs=2(rs). Since 1\" s is an integer, a b is even....

Q:

Find counterexamples to each of these statements about congruences. a) If ac bc (mod m), where a, b, c, and m are integers with m 2, then a b (mod m). b) If a b (mod m) and c d (mod m), where a,...

Q:

A small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The cross-sectional area of the coil is equal to S = 3.0 mm 2, the...

Q:

Describe about Herpes and HIV/AIDS

Q:

\ table [ [ MYRIAD PRODUCTS COMPANY Income Statement For the Year Ended December 3 1 , 2 0 2 4 ( $ in millions ) ] , [ Sales , , $ 9 0 0 ] , [ Cost of goods sold,, 3 1 5 ] , [ Gross margin,, 5 8 5 ]...

Q:

last two options for the multiple choice are : performance management development A construction equipment manufacturer, Roswell Corporation, is focusing on becoming a leader in sustainability in...

Q:

Some have speculated that in addition to increasing the validity of decisions, employing rigorous selection methods has symbolic value for organizations. What message is sent to applicants about the...

Q:

Discuss how the following trends are changing the skill requirements for managerial jobs in the United States: (a) increasing use of computers, (b) increasing international competition.

Q:

Does it have correct contact information?