Show that for any positive integer r, we can find integers m, n such that m2 - n2 = r3.
We notice that m2 - n2 = (m + n)(m - n). This suggests taking m + n = r2, m - n = r. This works: m = r(r + 1)/2, n = r(r - 1)/2.
14th Putnam 1954
© John Scholes
24 Nov 1999