MathDB

P(m_1) = P(m_2) = P(m_3) = P(m_4) = 7

Source: IMO Longlist 1989, Problem 78

September 18, 2008

algebrapolynomialalgebra unsolved

Problem Statement

Let

P(x)

be a polynomial with integer coefficients such that P(m_1) \equal{} P(m_2) \equal{} P(m_3) \equal{} P(m_4) \equal{} 7 for given distinct integers

m_1,m_2,m_3,

and

m_4.

Show that there is no integer m such that P(m) \equal{} 14.