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  • ...<math>p</math> can be represented as a sum of two nonzero [[perfect square|squares]] if and only if <math>p = 2</math> or <math>p \equiv 1 \pmod{4}</math>; an Fermat first listed this theorem in 1640, but listed it without proof, as was usual for him. Euler gave the
    4 KB (612 words) - 20:31, 7 January 2025
  • Four couples go ballroom dancing one evening. Their first names are H ...etween <math>1</math> and <math>2006</math>, inclusive, are perfect squares?
    31 KB (4,811 words) - 23:02, 3 November 2023
  • .../math> is a <math>10000000010</math>-degrees polynomial. The [[Fundamental Theorem of Algebra]] tells us that there are <math>10000000010</math> roots, say <m ...)</math>, where <math>b</math> and <math>c</math> are not divisible by the squares of any prime. Find <math>a^2+b^2+c^2+d^2+abcd</math>.
    64 KB (10,594 words) - 21:50, 9 January 2025