A grasshopper rests on the point (1,1) on the plane. Denote by O, the origin of coordinates. From that point, it jumps to a certain lattice point under the condition that, if it jumps from a point A to B, then the area of △AOB is equal to 21.
(a) Find all the positive integral poijnts (m,n) which can be covered by the grasshopper after a finite number of steps, starting from (1,1).
(b) If a point (m,n) satisfies the above condition, then show that there exists a certain path for the grasshopper to reach (m,n) from (1,1) such that the number of jumps does not exceed ∣m−n∣. geometrycalculusintegrationinductionmodular arithmeticcombinatorics unsolvedcombinatorics