Since 163 is a Heegner number, this mathematician’s constant, equal to e to the power of “pi root 163,” is remarkably close to an integer. For 10 points each:
[10m] Name this mathematician. A conversation between G. H. Hardy and this mathematician about the number 1729 led to the coining of the term “taxicab number.”
ANSWER: Srinivasa Ramanujan (“shree-nee-VAH-suh ra-MAH-noo-jun”) [accept Ramanujan constant]
[10h] Ramanujan’s constant is almost an integer because a degree-two instance of these constructs, formed by adjoining “root negative 163” to the rationals, has class number one. These constructs are finite extensions of the rationals.
ANSWER: algebraic number fields [prompt on fields; prompt on field extensions; prompt on quadratic fields by asking “can you be less specific?”]
[10e] In number fields with class number greater than one, this property and irreducibility are no longer equivalent in the associated ring of integers. The fundamental theorem of arithmetic concerns the factorization of an integer into numbers with this property.
ANSWER: primality [or primeness; or being prime]
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