MathDB

Let

a_{1}

\cdots

a_{k}

and

m_{1}

\cdots

m_{k}

be integers with

2 \le m_{1}

and

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

for

1 \le i \le k-1

. Show that there are infinitely many integers

x

which do not satisfy any of congruences

x \equiv a_{1}\; \pmod{m_{1}}, x \equiv a_{2}\; \pmod{m_{2}}, \cdots, x \equiv a_{k}\; \pmod{m_{k}}.

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