Any integer(s) which fulfill n^5 − 5n^3 + 5n + 1 ∣ n! ?


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Question Number 61782 by naka3546 last updated on 08/Jun/19

$A n y i n t e g e r (s) w h i c h f u l f i l l$ $n^{5} - 5 n^{3} + 5 n + 1 ∣ n! ?$
Commented by naka3546 last updated on 08/Jun/19

$p l e a s e s h o w w o r k i n g s!$
Commented by MJS last updated on 08/Jun/19

$again we can only try$
Commented by MJS last updated on 08/Jun/19

$n = 0$ $no other solution for n ⩽ 300$
Commented by naka3546 last updated on 08/Jun/19

$t h e r e w a s n s o h u g e t h a t f u l f i l l i t .$ $B u t, I {c a n}^{'} t s t i l l u n d e r s t a n d u n t i l n o w .$ $e . g : L e t X_{m} (n) = {(x^{n} + \frac{1}{x^{n}})}^{m}$ $f o r m = 5 . C o u l d a n y o n e e x p l a i n t o g e t t h a t e q u a t i o n i s ?$
Commented by naka3546 last updated on 08/Jun/19

$o r m a y b e l i k e t h i s$ $X_{m} (n) = {(x^{m} + \frac{1}{x^{m}})}^{n}$
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