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  • ...e assume that <math>z^{2000} + 1/z^{2000}</math> and <math>z^{2048} + 1/z^{2048}</math> has the same least integer greater than their solution. {{AIME box|year=2000|n=II|num-b=8|num-a=10}}
    4 KB (671 words) - 19:24, 2 November 2024
  • ...00</math> in base <math>2</math>. Therefore, <math>N = 8+16+32+64+256+512+2048+4096 \equiv 32 \pmod{1000}</math>, and the answer is <math>\boxed{032}</mat [https://youtu.be/d2UTg7OsYuE?si=-s4Ze-bsE2w-J5ij 2012 AIME II #7]
    2 KB (368 words) - 19:09, 19 July 2024
  • ===AIME styled=== (ii) No bigger rings are on top of smaller rings.
    64 KB (10,594 words) - 21:50, 9 January 2025