Triangular number theorem

The legacy record attributes to Gauss the discovery that every positive integer is representable as a sum of at most three triangular numbers, dated 10 July 1796 at Göttingen. No supplied passage states this theorem or its date directly, so the claim is retained only as legacy-attributed. The passages do confirm that Gauss studied at the University of Göttingen until 1798 under ducal patronage, that his mathematical diary records results beginning in 1796, and that he dated the start of his number-theory work to 1795, making a 1796 number-theoretic discovery consistent with the documented record.