If three square numbers form an arithmetic progression, then the gap between consecutive numbers in the progression (called a congruum) cannot itself be square. The only rational points on the elliptic curve y 2 = x ( x − 1 ) ( x + 1 ) {\displaystyle y^{2}=x(x-1)(x+1)} are the three trivial points with x ∈ { − 1 , 0 , 1 } {\displaystyle x\in \{-1,0,1\}} and y = 0 {\displaystyle y=0} . The quartic equation x 4 − y 4 = z 2 {\displaystyle x^{4}-y^{4}=z^{2}} has no nonzero integer solution.