triplets(p,x,y)

[man111]

Find all triples [tex](p, x, y)[/tex] such that [tex]px = y^4 + 4,[/tex] where [tex]p[/tex] is a prime and
[tex]x, y[/tex] are natural numbers.

[martin123456]

Let [tex]y^4+1=\prod_{i=1}^{n}p_i^{\alpha_i}[/tex], where [tex]p_i \in \mathbb{P}[/tex], [tex]\alpha_i \ge 1[/tex], [tex]n \ge 1[/tex].
Then all the triples are [tex](p_i, \frac{\prod_{i=1}^{n}p_i^{\alpha_i}}{p_i}, \prod_{i=1}^{n}p_i^{\alpha_i})[/tex].