Oblong numbers | O(a) + O(b) = O(c) – O(d)

 
 
An Oblong number is a number which is the product of two consecutive integers, that is, a number of the form   n \,(n + 1)

Let   O_n \; = \; n \,(n + 1)   be the n-th oblong number, for   n \; = \; 1, \; 2, \; 3, \; ...

Show that there are infinitely many pairs of distinct oblong numbers   O_a, \; O_b   and
O_c, \; O_d   with   c > d,   such that

O_a \; + \; O_b \; = \; O_c \; - \; O_d

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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