Oct 29, 2016 · I know that the sum of powers of $2$ is $2^{n+1}-1$, and I know the mathematical induction proof. But does anyone know how $2^{n+1}-1$ comes up in the first place. For …

I need some help with this problem: $$439^{233} \\mod 713$$ I can't calculate $439^{223}$ since it's a very big number, there must be a way to do this. Thanks.

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Feb 16, 2011 · I know that's an old thread but I had the same problem. I want to add a value to an existing average without having to calculate the total sum again. to add a value to an exisitng …

Mar 23, 2015 · In a drawer Sandy has 5 pairs of socks, each pair a different color. On Monday Sandy selects two individual socks at random from the 10 socks in the drawer. On Tuesday …

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With given N numbers only one of those numbers doesn't have pair, which one is it? After hours of surfing the net i found that XOR operator is good for that, because X xor X=0 X xor 0=X and …

Mar 25, 2016 · A friend of mine asked me how to derive the area and perimeter of a regular $n$-gon with a radius $r$ for a design project he is working on. I came up with this, but ...

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Why does squaring the radius of a circle times pi equal the area? (I.e., why does the area of circle representable as $\\pi r^2$ ?)What is the relationship between the radius of a circle and the area?