Find infinitely many triples (a,b,c) of distinct positive integers such that a, b, c are in arithmetic progression and ab+1,bc+1,ca+1 are perfect squares.

(     1,     8,   15) ;  (   15,     8,     1) ;
(     4,    30,   56) ;  (   56,    30,     4) ;
(    15,   112,  209) ;  (  209,   112,    15) ;
(    56,   418,  780) ;  (  780,   418,    56) ;
(   209,  1560, 2911) ;  ( 2911,  1560,   209) ;
(   780,  5822,10864) ;  (10864,  5822,   780) ;
    ...,   ...,  ...  ;     ...,   ...,   ...  ;

As it is given that there an infinite number of such triples, it would be impossible to list them all.

Posted by Dej Mar on 2018-03-26 04:08:14