Q: what's the 99th digit to the right of the decimal point in the decimal expansion of \( (1+\sqrt{2})^{500} \) ?? No spoilers!

· · CmdLineToot · 0 · 0 · 1

@ColinTheMathmo Do you have a nice method in mind? If so, can I have a hint?

@mscroggs Yes I have. Hmm. A hint. Here's a chance to learn about the "Content Warning" feature ...

Puzzle spoiler alert! 

@mscroggs Where there are sums and powers, there will always be, somehow, the difference of two squares.

Puzzle spoiler alert! 

@ColinTheMathmo Ok, that means I started along the right lines. Let's see where this goes....

@ColinTheMathmo This was a fun problem. A few minutes of play was enough to conjecture the correct answer, but it has taken me a while to come up with a complete proof.

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