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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

8 votes

Does the set $\{\binom x3+\binom y3+\binom z3:\ x,y,z\in\mathbb Z\}$ contain all integers?

Here are the representations (in a succinct form) of all the numbers in your list but $1523$. 522: -3132 -2827 3766 523: -1296 -576 1335 622: -3401 679 3394 633: -2446 -1646 2675 642: -2710 -2127 30 …
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