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For y coordinates see A201269.

For distances d between cubes and squares see A201268.

Primary points in A200656.

For definition primary points see A200656.

For secondary terms in A200656 see A201048.

For successive quadratic extensions see A201278.

Theorem (*Artur Jasinski*):

Every particular coordinate x contained only one extremal point.

Proof (*Artur Jasinski*): Coordinate y is computable from the formula y(x) = round(sqrt(x^3)) and distance d between cube of x and square of y is computable from the formula d(x) = x^3-(round(sqrt(x^3)))^2.

For successive x coordinates see A201047.

For successive y coordinates see A201269.

One elliptic curve with particular d can contain a finite number of extremal points.

Theorem (*Artur Jasinski*):

One elliptic curve cannot contain more than 1 extremal primary point with quadratic extension over rationals.

Consequence of this theorem is that any number in this sequence can't appear more than 1 time.

Conjecture (*Artur Jasinski*):

One elliptic curve cannot contain more than 1 point with quadratic extension over rationals.

Mordell elliptic curves contained points with extensions which are roots of polynomials : 2 degree (with Galois 2T1), 4 degree (with Galois 4T3) and 6 degree (with not soluble Galois PGL(2,5) ). Order of minimal polynomial of any extension have to divided number 12. Theoretically points can exist which are roots of polynomial of 3 degree but any such point isn't known yet.

Particular elliptic curves x^3-y^2=d can contain more than one extremal point e.g. curve x^3-y^2=-297=a(8) contained 3 of such points with coordinates x={48, 1362, 93844}={A134105(7),A134105(8),A134105(9)}.

Conjecture (*Artur Jasinski*): Extremal points are k-th successive points with maximal coordinates x.