n(n+1)(n+2)(n+3)+1
= (n²+n)(n²+5n+6)+1
= n^4+5n³+6n²+n³+5n²+6n+1
= n^4+6n³+11n²+6n+1

(n²+an+1)² = n^4+a²n²+1+2an³+2n²+2an
(n²+an+1)² = n^4+2an³+n²(a²+2)+2an+1
a=3 convient pour que n^4+6n³+11n²+6n+1 = n^4+2an³+n²(a²+2)+2an+1

--> n(n+1)(n+2)(n+3)+1 = (n²+3n+1)²
-----
Sauf distraction.