statement.html

problem 46 · 13 lines

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<p>It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.</p>
$$\begin{align}
9 = 7 + 2 \times 1^2\\
15 = 7 + 2 \times 2^2\\
21 = 3 + 2 \times 3^2\\
25 = 7 + 2 \times 3^2\\
27 = 19 + 2 \times 2^2\\
33 = 31 + 2 \times 1^2
\end{align}$$
<p>It turns out that the conjecture was false.</p>
<p>What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?</p>
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