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In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation a n + b n = c n for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions. [1]
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The last case is if ρ(E, 3) is reducible and ρ(E, 5) is irreducible. Wiles showed that in this case, one could always find another semistable elliptic curve F such that the representation ρ ( F , 3) is irreducible and also the representations ρ ( E , 5) and ρ ( F , 5) are isomorphic (they have identical structures).
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SPOILERS BELOW—do not scroll any further if you don't want the answer revealed. The New York Times. Today's Wordle Answer for #1298 on Tuesday, January 7, 2025.
The husband is always the last to know; The innocent seldom find an uncomfortable pillow – William Cowper, English poet (1731–1800) [28] The labourer is worthy of his hire; It is the last straw that breaks the camel's back; The law is an ass (from English writer Charles Dickens' novel Oliver Twist) The leopard does not change his spots
In another notable Times crossword, 27-year-old Bill Gottlieb proposed to his girlfriend, Emily Mindel, via the crossword puzzle of January 7, 1998, written by noted crossword constructor Bob Klahn. [ 55 ] [ 56 ] The answer to 14-Across, [Microsoft chief, to some] was BILLG, also Gottlieb's name and last initial. 20-Across, [1729 Jonathan Swift ...
Groups of puzzles in a puzzle hunt are often connected by a metapuzzle, which is a puzzle based on combining or comparing the answers of other ("feeder") puzzles. For some metapuzzles (sometimes called "shell" metapuzzles), the answers to the feeder puzzles must be incorporated into a puzzle structure that is separately provided to solvers; for ...