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2021-08-12, 13:11   #5
charybdis

Apr 2020

12768 Posts

Quote:
 Originally Posted by Dr Sardonicus The sum of fractions with a common factor in the denominator can be a fraction without that factor in the denominator, e.g. 1/3 + 1/6 = 1/2. In fact, the common factor can show up in the numerator of the sum!
This reminds me of another fun problem: show that every rational between 0 and 1 can be represented as the sum of reciprocals of distinct positive integers.

Quote:
 Originally Posted by bur (how do you produce a # in Tex here? \# or \text{#} didn't work...)
Like this: $$\#$$

Or like this:
$\frac{1}{p_1}+\frac{1}{p_2}+\frac{1}{p_3}=\frac{p_1p_2+p_1p_3+p_2p_3}{p_3\#}$