2015/113) There is a number n between to successive squares.this is k larger than the smaller number and l smaller than the larger number . Prove that n-kl is a perfect square.

Let the number n be between $a^2$ and $(a+1)^2$
As per given condition
$n- a^2 = k\cdots(1)$
$(a+1)^2 –n = l\cdots(2)$
Adding (1) and (2)
$k + l = 2a + 1$
or $l = 2a + 1 - k$
now
$n- kl = (a^2+k) – k(2a+1-k)
= a^2 + k – 2ak –k + k^2 = a^2 – 2ak + k^2 = (a-k)^2$
Hence proved