Any-integer-s-which-fulfill-n-5-5n-3-5n-1-n-

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}