Question

If a, b are positive integers such that a < b and $\left[ab\right]\left[\begin{array}{c}a\\ b\end{array}\right]=25,$ then (a, b) = ____________.

Answer 1

$\left[ab\right]\left[\begin{array}{c}a\\ b\end{array}\right]=\left[25\right]$

$\Rightarrow \left[a^2+b^2\right]=\left[25\right]$

$\Rightarrow a^2+b^2=25$

Now,

$3^2+4^2=5^2=25$

∴ a = 3 and b = 4 (a < b)

Thus, the ordered pair (a, b) is (3, 4).

If a, b are positive integers such that a < b and $\left[ab\right]\left[\begin{array}{c}a\\ b\end{array}\right]=25,$ then (a, b) = ___(3, 4)___.