Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).

Prove that the coordinates of the vertices of an equilateral triangle can not all be rational.

The number of integral point inside the triangle made by the line 3x + 4y - 12 =0 with the coordinate axes which are equidistant from at least two sides is/are : ( an integral point is a point both of whose coordinates are integers. )

The number of integral points inside the triangle made by the line 3x+4y-12=0 with the coordinate axes which are equidistant from at least two sides is/are (an integral point is a point both of whose coordinates are integers.) (d) 4(c)3(a)1 (b) 2

Let f(r) be the number of integral points inside a circle of radius r and centre at origin (integral point is a point both of whose coordinates are integers),then lim_(r rarr oo)(f(r))/(pi r^(2)) is equal to

A point both of whose coordinates are negative lies in quadrant

If two vertices of an equilaterla triangle have integral coordinates, then the third vetex will have

Let C be any circle with centre ( 0, sqrt( 2)) . Prove that at most two rational points can be there on C. ( A rational point is a point both of whose coordinates are rational numbers . )

The number of integral points on the hyperbola x^(2)-y^(2)=(2000)^(2) is (an integral point is a point both of whose co-ordinates are integer) (A) 98(B)96(C)48(D)24