MathDB

Turkish MO 1995 P1

Source: Turkish Mathematical Olympiad 2nd Round 1995

September 30, 2006

number theory unsolvednumber theory

Problem Statement

Let

m_{1},m_{2},\ldots,m_{k}

be integers with

2\leq m_{1}

and

2m_{1}\leq m_{i+1}

for all

i

. Show that for any integers

a_{1},a_{2},\ldots,a_{k}

there are infinitely many integers

x

which do not satisfy any of the congruences

x\equiv a_{i}\ (\bmod \ m_{i}),\ i=1,2,\ldots k.