[Q]: Question: "How does the idea change?" Context: "for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the etale fundamental group." Answer:
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[A]: An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the etale fundamental group

input: Please answer the following: Question: "What does a king wear?" Context: "One of John's principal challenges was acquiring the large sums of money needed for his proposed campaigns to reclaim Normandy. The Angevin kings had three main sources of income available to them, namely revenue from their personal lands, or demesne; money raised through their rights as a feudal lord; and revenue from taxation. Revenue from the royal demesne was inflexible and had been diminishing slowly since the Norman conquest. Matters were not helped by Richard's sale of many royal properties in 1189, and taxation played a much smaller role in royal income than in later centuries. English kings had widespread feudal rights which could be used to generate income, including the scutage system, in which feudal military service was avoided by a cash payment to the king. He derived income from fines, court fees and the sale of charters and other privileges. John intensified his efforts to maximise all possible sources of income, to the extent that he has been described as "avaricious, miserly, extortionate and moneyminded". John also used revenue generation as a way of exerting political control over the barons: debts owed to the crown by the king's favoured supporters might be forgiven; collection of those owed by enemies was more stringently enforced." Answer:
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output: crown

Please answer this: Question: "What type of object was the atomic bomb?" Context: "Von Neumann's principal contribution to the atomic bomb was in the concept and design of the explosive lenses needed to compress the plutonium core of the Fat Man weapon that was later dropped on Nagasaki. While von Neumann did not originate the "implosion" concept, he was one of its most persistent proponents, encouraging its continued development against the instincts of many of his colleagues, who felt such a design to be unworkable. He also eventually came up with the idea of using more powerful shaped charges and less fissionable material to greatly increase the speed of "assembly"." Answer:
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Answer: weapon

Problem: Question: "citation was said to be?" Context: "Broadly speaking, government phonology (or its descendant, strict-CV phonology) has a greater following in the United Kingdom, whereas optimality theory is predominant in the United States.[citation needed]" Answer:

A: needed

Problem: Given the question: Question: "What kind of objects could be pieces of art in themselves?" Context: "Lighting fixtures come in a wide variety of styles for various functions. The most important functions are as a holder for the light source, to provide directed light and to avoid visual glare. Some are very plain and functional, while some are pieces of art in themselves. Nearly any material can be used, so long as it can tolerate the excess heat and is in keeping with safety codes." Answer:
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The answer is:
Lighting fixtures

Problem: Question: "What achievement has a number usually associated with bad luck?" Context: "Notre Dame rose to national prominence in the early 1900s for its Fighting Irish football team, especially under the guidance of the legendary coach Knute Rockne. The university's athletic teams are members of the NCAA Division I and are known collectively as the Fighting Irish. The football team, an Independent, has accumulated eleven consensus national championships, seven Heisman Trophy winners, 62 members in the College Football Hall of Fame and 13 members in the Pro Football Hall of Fame and is considered one of the most famed and successful college football teams in history. Other ND teams, chiefly in the Atlantic Coast Conference, have accumulated 16 national championships. The Notre Dame Victory March is often regarded as the most famous and recognizable collegiate fight song." Answer:

A:
13 members in the Pro Football Hall of Fame