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Given a question as follows.

Find the greatest $x$ that divides 14, 19, 25, 52 and leaves remainders 4, 1, 5 and 2, respectively.

For me this question does not make sense. Because the $\text{HCF}$ of $14-4$, $19-1$, $25-5$, and $52-2$ is $\text{HCF}(10,18,20,50)=2$.

Here if $x=2$ then it divides 14 without remainder. But the question said its remainder is 4. Or I am wrong?

Question

How to properly explain that this question does not make sense?

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    $\begingroup$ @LukasKofler: 2 divides 14 without remainder. $\endgroup$ – Well Harassed Programmer Aug 22 at 14:26
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    $\begingroup$ @MoneyOrientedProgrammer It could: $14 = 5\cdot 2 + 4$. Depending on how your problem author meant "leaves remainder". It's not standard, but it's conceivable. $\endgroup$ – Arthur Aug 22 at 14:26
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    $\begingroup$ @Arthur So, the question could be rephrased as $14\equiv4\pmod{x}$ and so forth? $\endgroup$ – saulspatz Aug 22 at 14:30
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    $\begingroup$ You are right $-$ the question makes no sense. $\endgroup$ – TonyK Aug 22 at 14:32
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    $\begingroup$ The only numbers that divide 14 with a remainder of 4 are 5 and 10. They do not satisfy the other conditions, so there is no solution. $\endgroup$ – Gabe Aug 22 at 14:58

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