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Four positive binary squares conjecture
Four positive binary squares conjecture. Every natural number $N>1772$ is the sum of exactly four positive binary squares. The $112$ exceptions are
Conjectureopenadditive-number-theory binary-squares number-theoryarXiv posted 3 days ago
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Density conjecture for sums of three binary squares
Density conjecture. The lower asymptotic density satisfies
Conjectureopenasymptotic-density binary-squares number-theoryarXiv posted 3 days ago

Four positive binary squares conjecture