But of course, the numbers aren't necessarily distinct, so that's an extra wrinkle. At least this reduces the problem into determining whether number of the form 2T, where T is a triangular number, can be represented by 2 or more other triangular numbers.

@Michael Mendrin
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This definitely cannot be done for some numbers. For example 5 = 3 + 1 + 1, but there is no expression for it in terms of unique triangular numbers.
–
Marta Reece
·
4 months, 3 weeks ago

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Fermat Polygonal Number Theorem

But of course, the numbers aren't necessarily distinct, so that's an extra wrinkle. At least this reduces the problem into determining whether number of the form 2T, where T is a triangular number, can be represented by 2 or more other triangular numbers.

– Michael Mendrin · 4 months, 3 weeks ago

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– Marta Reece · 4 months, 3 weeks ago

This definitely cannot be done for some numbers. For example 5 = 3 + 1 + 1, but there is no expression for it in terms of unique triangular numbers.Log in to reply