Task: Data Analysis / DocumentQA
User instruction:
The greatest giant of mathematics, Gauss, was born in Braunschweig, Germany, into a poor family whose father baked bricks. Because Gauss’s father had not received a proper school education, he considered scholarship useless and wanted his son to follow him as a brick laborer. However, Gauss loved studying and often quarreled with his father during his childhood. His mother, however, was supportive of Gauss’s studies, and so was his uncle. Thanks to the support of his mother and uncle, Gauss was able to study diligently, although his father gave no support. Later, with the backing of the Duke of Brunswick, he was able to study from 1792 to 1795 at the Carolinum (Latin: Collegium Carolinum, now the Technical University of Braunschweig). Afterwards, again with the duke’s help, he transferred to the University of Göttingen, where he stayed from 1795 to 1798. At Göttingen, Gauss independently rediscovered several important theories.
In 1796 Gauss showed that a regular polygon whose number of sides is a Fermat prime can be constructed with only a straightedge and compass. In particular, on March 30 he discovered that a regular 17-gon can be constructed. This was a very important discovery in the classical problem of geometric construction, which had been central to mathematics since ancient Greece. Later, Gauss was so delighted by this result that, just as Archimedes had a sphere inscribed in a cylinder carved on his tombstone and Jakob Bernoulli had a logarithmic spiral carved on his, he asked that a 17-gon be carved on his own; but because it would have been hard to distinguish from a circle, a star with 17 points was carved instead.
Gauss also discovered the arithmetic of congruences in number theory and, on April 8, 1796, gave the first proof of the law of quadratic reciprocity. This astonishing general law enabled mathematicians to determine the solvability of quadratic equations. On May 31, 1796, the conjectured prime number theorem helped to understand how prime numbers are distributed among the integers. In addition, on July 10 he proved that every natural number can be represented as the sum of three triangular numbers, leaving the famous diary entry “Heureka! num = Δ + Δ + Δ.” On October 1, 1796, he published his results on the number of solutions of equations in finite fields according to their coefficients.
He completed his representative work, Disquisitiones Arithmeticae, in 1798 at the age of 21, although it was not published until 1801.
Find and explain all of Gauss’s contributions to number theory mentioned in the above text.

Evaluation criteria:
You must explain all number-theoretical contributions mentioned in the original text, including congruence arithmetic, the law of quadratic reciprocity, the prime number theorem, representations by triangular numbers.
You must answer in the same language as the input.