Sidon sequence

<p>In <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, a Sidon sequence is a sequence 
  
    
      
        A
        =
        {
        
          a
          
            0
          
        
        ,
        
          a
          
            1
          
        
        ,
        
          a
          
            2
          
        
        ,
        …
        }
      
    
    {\displaystyle A=\{a_{0},a_{1},a_{2},\dots \}}
  
 of natural numbers in which all pairwise sums 
  
    
      
        
          a
          
            i
          
        
        +
        
          a
          
            j
          
        
      
    
    {\displaystyle a_{i}+a_{j}}
  
 (for 
  
    
      
        i
        ≤
        j
      
    
    {\displaystyle i\leq j}
  
) are different. Sidon sequences are also called Sidon sets; they are named after the Hungarian mathematician <a href="/facts/Simon_Sidon/SJn3UGal">Simon Sidon</a>, who introduced the concept in his investigations of <a href="/facts/Fourier_series/s3fsxPAT">Fourier series</a>.
</p><p>The main problem in the study of Sidon sequences, posed by Sidon, is to find the maximum number of elements that a Sidon sequence can contain, up to some bound 
  
    
      
        x
      
    
    {\displaystyle x}
  
.  Despite a large body of research, the question has remained unsolved.
</p>

Sidon sequence open-in-new

Sidon sequence