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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....

Matthew Scroggs@mscroggs@mathstodon.xyz@ColinTheMathmo Do you have a nice method in mind? If so, can I have a hint?