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What is the slowest-growing non-repeating, non-trivial* whole number sequence? [more inside]

For a work assignment, I need to come by a conceptual understanding of modular forms that's light on jargon and, ahem, actual math. If such a thing is possible.

Is there a closed-form method for finding the unique subsets from the power set of prime factors of an integer? [more inside]

I'm an algebraist, and I need help with a difficult number theory problem involving Mersenne Numbers. Difficult Number Theorists, please help me! [more inside]

This page mentions, among other things, that "100 is the smallest square which is also the sum of 4 consecutive cubes." Obviously, this refers to the sum of 1^3 (1), 2^3 (8), 3^3 (27) and 4^3 (64). But it seems to me that the sequence can be pushed back to start with 0^3 (0), in which case you can get four consecutive cubes adding up to 36, which is a square. Is zero then not considered a cube? [more inside]

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