MathDB

integral roots

Source: All Russian Mathematical Olympiad 2008. 11.5

June 13, 2008

calculusintegrationinequalitiesnumber theory proposednumber theory

Problem Statement

The numbers from

51

150

are arranged in a

10\times 10

array. Can this be done in such a way that, for any two horizontally or vertically adjacent numbers

a

and

b

, at least one of the equations x^2 \minus{} ax \plus{} b \equal{} 0 and x^2 \minus{} bx \plus{} a \equal{} 0 has two integral roots?