Given that N2 + 5N + 13 is a complete square number, then the value of natural number n is______ ．

Suppose: N2 + 5N + 13 = (n + k) 2, ｜ (n + k) 2 = N2 + 2nk + K2, ｜ 2nk + K2 = 5N + 13, ｜ n = K2 − 135 − 2K, if n is a natural number, then it should not be less than 0 (it is not equal to 0 from the formula), ｜ ① K2 > 13 and 5 > 2K (does not exist); ② K2 < 13 and 5 < 2K, only k = 3, then n = 4

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