Problem 1.  Evaluate the following expressions:     (a) 8  (mod 3) =  (d) 22  (mod 11) =           (b) 17  (mod 8) =   (e) −17  (mod 8) =           (c) 7  (mod 12) =   (f ) 0  (mod 9) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 1.  Evaluate the following expressions:

 

 

(a) 8  (mod 3) = 

(d) 22  (mod 11) =  

 

 

 

 

(b) 17  (mod 8) =  

(e) −17  (mod 8) =  

 

 

 

 

(c) 7  (mod 12) =  

(f ) 0  (mod 9) =  

 

 

 

Problem 2.  Evaluate the expressions in each of the following triples:

 

 

(a)        8    (mod 3)        =      12    (mod 3)      =        8 + 12    (mod 3)      =

 

 

(b)        7    (mod 5)        =      23    (mod 5)      =     7 + 23    (mod 5)      =

 

 

(c)        3    (mod 4)        =       10    (mod 4)      =   3 · 10    (mod 4)        =   

 

 

(d)        16    (mod 10)    =   11    (mod 10)    =      16 · 11    (mod 10)    =   

 

What  conclusions can you draw?

 

 

 

 

 

 

 

 

 

Problem 3.  Evaluate the following (please do not use a calculator): (a) 11 · 11 · 11 · 11 · 11  (mod 10) =  

 

 

(b) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15  (mod 2) =  

 

 

(c) 2100   (mod 3)

 

 

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