A number theory problem by Kaleem Kħặŋ

The Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones:

$1,1,2,3,5,8,13,21,34,55,89,$ $\color{#D61F06}\boxed{144}$ $,233,377,610 ...$

From the above, the smallest number greater than $1$ which is a perfect square is $144$ .

It is easy to find the smallest perfect square between the Fibonacci numbers:

Fibonacci Numbers:

$1,1,2,3,5,8,13,21,34,55,89,\boxed{144},233,\cdots$

Perfect squares:

$1,4,9,16,25,36,49,64,81,100,121,\boxed{144},169,\cdots$

It is just a matter of inspecting Fibonacci numbers.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233

and picking out a square from these.

144 is12^2