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For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.
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 …