Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers
In general (m2 - n2) = (m + n)(m - n) so if m = n+1 we have
(m2 - n2) = ((n+1)2 - n2) = (n+1 + n)(n+1 - n) = (m + n)*1 = m + n
.
