Track / Stage 4 / 107 of 340 #367 of 1964

Let $g$ be a natural number, and $g^{4}+g^{3}+g^{2}+g+1$ is a perfect square, then the sum of all such $g$ is $\qquad$ .

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A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

2. Solving $g^{2}-2 g-3=0$ yields $g=3$, so there is only one such $g$, which is 3.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.