Roots are x = 2 and x = 3.

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Try small values modulo 5 first:Mod 5: \(n^3 \equiv 13 \equiv 3 \pmod{5}\)Check cubes mod 5:\(0^3 = 0\)\(1^3 = 1\)\(2^3 = 8 \equiv 3\)\(3^3 = 27 \equiv 2\)\(4^3 = 64 \equiv 4\)So only \(n \equiv 2 \pmod{5}\) works.Now lift to mod 25: Let \(n = 5k + 2\). Plug into \(n^3 \equiv 13 \pmod{25}\):