1729
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$${\rm Published}$$ $${\rm Online}$$ $${\rm First}$$ $${(2/17/2025)}$$
$${\rm Latest}$$ $${\rm additions}$$ $${(2/17/2025)}$$
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$${\bf 1729}$$は「自身の$${4}$$乗の$${2}$$倍」が「$${3}$$個の$${4}$$乗数の和」として「$${13}$$通り」に表せる最小数である.
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$${\begin{aligned}2･1729^4&=1995^4+1064^4+931^4\\&=1989^4+1144^4+845^4\\&=1984^4+1185^4+799^4\\&=1976^4+1235^4+741^4\\&=1961^4+1305^4+656^4\\&=1960^4+1309^4+651^4\\&=1925^4+1421^4+504^4\\&=1911^4+1456^4+455^4\\&=1881^4+1520^4+361^4\\&=1859^4+1560^4+299^4\\&=1840^4+1591^4+249^4\\&=1824^4+1615^4+209^4\\&=1775^4+1679^4+96^4 \end{aligned}}$$
$${\small \rm (Takao \<space> Nakamura, 2/17/2025)}$$
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$${REFERENCES}$$
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