Squares & Oblong numbers| 1*2 – 2*3 + 3*4 – 4*5 + … + (-1)^(n-1) n(n+1)

 
 
An Oblong number is a number of the form   n \,(n + 1)
 
 

Let   A_n \; = \; (1\times 2) \; - \; (2\times 3) \; + \; (3\times 4) \; - \; (4\times 5) \; + \; ... \; + \; (-1)^{n-1} \; n \,(n+1)
 

Determine the values of   n   for which

(1)   2 \; \times \; \; A_n   is a square number

(2)   1/2 \; \times \; \; |A_n|   is an Oblong number

 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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