MathDB
trinomial and consecutive natural numbers

Source: 9th-th Hungary-Israel Binational Mathematical Competition 1998

July 13, 2007
calculusintegrationnumber theory proposednumber theory

Problem Statement

Let a,b,c,m,n a, b, c, m, n be positive integers. Consider the trinomial f(x)=ax2+bx+c f (x) = ax^{2}+bx+c. Show that there exist n n consecutive natural numbers a1,a2,...,an a_{1}, a_{2}, . . . , a_{n} such that each of the numbers f(a1),f(a2),...,f(an) f (a_{1}), f (a_{2}), . . . , f (a_{n}) has at least m m different prime factors.
Back to ProblemsView on AoPS