Prove that the product of 4 consecutive positive integers cannot be a perfect square.
Given an infinite number of points in a plane, prove that if all the distances determined between them are integers, then the points are all in a straight line.
Prove that every positive integer has a multiple whose decimal representation involves all ten digits.
Show that if the differential equation
is both homogeneous and exact, then the solution y = f(x) satisfies xM + yN = C (constant).
A sphere rolls along two intersecting straight lines. Find the locus of its center.
Determine all polynomials P(x) such that P(x2+1) = (P(x))2 + 1 and P(0) = 0.