C hope that helped have a great time I love it you can do
        
                    
             
        
        
        
Answer:
1 2 3 6 7 14 21 42Step-by-step explanation:
all of them are divisible by 42
 
        
                    
             
        
        
        
Answer:
Proofs are in the explantion. 
Step-by-step explanation:
We are given the following:
1)  for integer
 for integer  .
.
1)  for integer
 for integer  .
.
a) 
Proof:
We want to show  .
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(a+c)-(b+d)=rn. If we do that we would have shown that  .
.
kn+mn   =  (a-b)+(c-d) 
(k+m)n   =   a-b+ c-d
(k+m)n   =   (a+c)+(-b-d)
(k+m)n  =    (a+c)-(b+d)
k+m is is just an integer 
So we found integer r such that (a+c)-(b+d)=rn.
Therefore,  .
.
//
b) Proof:
We want to show  .
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(ac)-(bd)=tn. If we do that we would have shown that  .
.
If a-b=kn, then a=b+kn.
If c-d=mn, then c=d+mn.
ac-bd  =  (b+kn)(d+mn)-bd
           =    bd+bmn+dkn+kmn^2-bd
           =           bmn+dkn+kmn^2
           =            n(bm+dk+kmn)
So the integer t such that (ac)-(bd)=tn is bm+dk+kmn.  
Therefore,  .
.
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