Some arithmetic of elliptic curves and theory of elliptic surfaces is used to find all rational solutions (r, s, t) in the function field Q(m, n) of the pair of equations r(r + 1)/2 = ms(s + 1)/2 r(r + 1)/2 = nt(t + 1)/2. It turns out that infinitely many solutions exist. Several examples will be given.
|Number of pages||13|
|Journal||Rocky mountain journal of mathematics|
|Publication status||Published - 1996|