Prove that for all positive integers m and n, there is a positive integer k such that \[ (\sqrt{m}+\sqrt{m-1})^n = \sqrt{k}+\sqrt{k-1}.\]
KAIST Math Problem of the Week
Weekly Math Challenges in KAIST
Prove that for all positive integers m and n, there is a positive integer k such that \[ (\sqrt{m}+\sqrt{m-1})^n = \sqrt{k}+\sqrt{k-1}.\]