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Q: what's the 99th digit to the right of the decimal point in the decimal expansion of \( (1+\sqrt{2})^{500} \) ?? No spoilers!
@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.
@ColinTheMathmo Do you have a nice method in mind? If so, can I have a hint?