Hkimo Past Papers Senior Secondary |link|

At first glance, a student might try factoring: ((n+4)(n+5)). But that does not help for perfect squares. The solution requires setting ( n^2+9n+20 = k^2 ), then rearranging to ( (2n+9)^2 - (2k)^2 = 1 ), turning it into a Pell-like equation. This is classic HKIMO: a simple expression hiding a deep number theory concept.

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