MathDB

5

Part of 1998 Irish Math Olympiad

Problems(2)

prove that x is an integer

Source: Ireland 1998

7/4/2009
If x x is a real number such that x^2\minus{}x and x^n\minus{}x are integers for some n≥3 n \ge 3, prove that x x is an integer.
algebrapolynomialnumber theory unsolvednumber theory
minimum possible perimeter

Source: Ireland 1998

7/4/2009
A triangle ABC ABC has integer sides, \angle A\equal{}2 \angle B and ∠C>90∘ \angle C>90^{\circ}. Find the minimum possible perimeter of this triangle.
geometryperimeterAMCUSA(J)MOUSAMOgeometry proposed