A graph of Y=X
^{3} 2017X shows the characteristic cubic form. N will just shift it up or down. What we seek is the value of N that will make all solutions integers.
This is equivalent to finding three values of X in the above equation that give the same value of Y. From the graph, these must be in the interval [51,51].
What I did was make a take of X,Y and then sorted by Y. A quick scan found only one triple repeat of Y.
(48,13776), (7,13776), (41,13776)
(There were also no duplicates.)
This implies the solution 48+7+41=96 and also
X
^{3} 2017X+13776=(X+48)(X7)(X41)

Posted by Jer
on 20160622 13:37:44 