Cauchy's Criterion for the Solvability of Xp + YpZp in Integers Prime to P

Cauchy stated, and it is not yet prqred, that if the equation X^p + Y^{p =} Z^p has any solutions in integers all prime to p, then

^θ∑_n=1 n^p-4=O(mod p) … (1.1)

where θ= [¹/₂p]; [x] denotes the greatest integer contained in.