Hint to puzzle 71: Consecutive cubes and squares
If (m + 1)3 − m3 = n2, show that 3(2m + 1)2 = (2n − 1)(2n + 1). Then use the fact that 2n − 1 and 2n + 1 are relatively prime.
If (m + 1)3 − m3 = n2, show that 3(2m + 1)2 = (2n − 1)(2n + 1). Then use the fact that 2n − 1 and 2n + 1 are relatively prime.