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Question: $\boxed{\text{Consider $\sum_{i=1}^{100}\tfrac{1}{i}=\tfrac{A}{B}$. Given that $\text{gcd}(A,B)=1$, Show that $5\nmid AB$}}$

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    If you use least common multiples, the denominator has only two factors of $5$ in it – 2017-01-02
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    The question doesn't say that $5 \not\mid AB$. It asks you to determine whether $5 \mid AB$ or $5 \not\mid AB$. It seems that you have determined that $5 \mid AB$. – 2017-01-02
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    @JimmyK4542 Well, well, the question said to show $5$ doesn't divide $AB$. Here, I have written the question differently to pose in front of you people. Anyway, I am editing it. – 2017-01-02
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    Numerical computations suggest that $5\nmid AB$, and that $AB\pmod{5} = 2$. – 2017-01-02
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    Based on this [Wolfram Alpha query](http://www.wolframalpha.com/input/?i=sum+1%2Fn+from+n+%3D+1+to+100), it seems that $A$ and $B$ are not divisible by $5$. – 2017-01-02
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    @JimmyK4542 It asks if their product is divisible or not. You claim that none of them is divisible right? Can you give me a reason? – 2017-01-02
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    All I did was type that sum into Wolfram Alpha and look at the fraction it gave as the answer. I have no mathematical justification to show that $5 \not\mid AB$. – 2017-01-02
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    Oh okay, fine fine – 2017-01-02
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    Okay, then no more solutions be posted. Thanks. – 2017-01-02

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