[Number Theory] Find n from n²

[@realcirno1750]

(n+1)^2 = n^2 + 2n + 1 = n^2 + 2(n+1) - 1 so n^2 = 1 (mod n+1) so n^2 + 1 = 2 (mod n+1) hence if n+1 | n^2+1, then 2 = 0 (mod n+1) so 2 = k(n+1) so n+1 is a factor of 2 so n+1 = 2, n+1 = 1, n+1=-1 or n+1=-2 since n is natural, n+1 = 2 so n=1