Proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers
2019 ◽
Vol 15
(01)
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pp. 189-212
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Keyword(s):
In a recent paper, Sun posed six conjectures on the relations between [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the number of representations of [Formula: see text] as [Formula: see text], where [Formula: see text] are positive integers, [Formula: see text] are arbitrary nonnegative integers, and [Formula: see text] denotes the number of representations of [Formula: see text] as [Formula: see text], where this time [Formula: see text] are integers. In this paper, we prove Sun’s six conjectures by using Ramanujan’s theta function identities.
2020 ◽
Vol 16
(06)
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pp. 1275-1294
2020 ◽
Vol 102
(1)
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pp. 39-49
2018 ◽
Vol 14
(07)
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pp. 1995-2011
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2020 ◽
Vol 9
(7)
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pp. 4929-4936
2021 ◽
Vol 14
(2)
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pp. 380-395