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The two first subsections, are proofs of the generalized version of Euclid's lemma, namely that: if n divides ab and is coprime with a then it divides b. The original Euclid's lemma follows immediately, since, if n is prime then it divides a or does not divide a in which case it is coprime with a so per the generalized version it divides b.
The first, from an 1870 publication, is "Best Turkey opium 1 oz., slice, and pour upon it boiling water 1 gill, and work it in a bowl or mortar until it is dissolved; then pour it into the bottle, and with alcohol of 70 percent proof 1 ⁄ 2 pt., rinse the dish, adding the alcohol to the preparation, shaking well, and in 24 hours it will be ...
Projection of the Kardashev scale to 2040 based on data from the International Energy Agency World Energy Outlook. Kardashev presented for the first time a classification of civilizations according to the level of the rate of their energy consumption, or ability to harness power, in an article entitled Transmission of Information by Extraterrestrial Civilizations, published in 1964 first in ...
Performed by Frank Oz (1976–2000), Eric Jacobson (2001–present); A temperamental diva pig who is the Muppets' break-out and "authentic superstar". [1]: 28 Until 2015, she was the romantic significant other of Kermit.
the corruption of the best is the worst: corruptissima re publica plurimae leges: When the republic is at its most corrupt the laws are most numerous: Tacitus: corvus oculum corvi non eruit: a raven does not pick out an eye of another raven: corruptus in extremis: corrupt to the extreme: Motto of the fictional Mayor's office in The Simpsons
This list of countries by life expectancy provides a comprehensive list of countries alongside their respective life expectancy figures. The data is differentiated by sex, presenting life expectancies for males, females, and a combined average.
TRAPPIST-1 TRAPPIST-1 is within the red circle in the constellation Aquarius. Observation data Epoch J2000 Equinox J2000 Constellation Aquarius Right ascension 23 h 06 m 29.368 s Declination −05° 02′ 29.04″ Apparent magnitude (V) 18.798 ± 0.082 Characteristics Evolutionary stage Main sequence Spectral type M8V Apparent magnitude (R) 16.466 ± 0.065 Apparent magnitude (I) 14.024 ± 0. ...