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For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 ≡ 4 (mod 6). Equivalently, n − 1 / 3 ≡ 1 (mod 2) if and only if n ≡ 4 (mod 6). Conjecturally, this inverse relation forms a tree except for the 1–2–4 loop (the inverse of the 4–2–1 loop of the unaltered function f defined in the Statement of the problem section of ...
On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. This is the easier part of the theorem, and follows immediately from the observation that all squares are congruent to 0 (if number squared is even) or 1 (if number squared is odd) modulo 4.
1992, for regularly scheduled new panels. Occasional new panels from 1997-2012. Syndicate (s) United Feature Syndicate. Genre (s) Humor, gag-a-day, satire, adults. Herman is a comic strip written and drawn by Jim Unger. While the daily ran as a single panel with a typeset caption, it expanded every Sunday as a full multi-panel strip with balloons.
[1] For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0. Although typically performed with a and n both being integers, many computing systems now allow other types of numeric ...
978-1-62779-446-6. 4 3 2 1 is a 2017 novel by Paul Auster published by Henry Holt and Co. It describes four alternate versions of the life of Archie Ferguson in the 1950s and 1960s, and explores how an individual's life and personality is shaped by chance and circumstance. In September 2017 it was shortlisted for the 2017 Man Booker Prize. [1]
Herman and Katnip is a series of theatrical cartoons featuring Herman the Mouse and Katnip the Cat, produced by Famous Studios in the 1940s and 1950s. [1] Arnold Stang and Allen Swift were the regular voices of Herman, [ 2 ] while Sid Raymond was the regular actor for Katnip, although one or both of the characters would occasionally be voiced ...
The Ages of Three Children puzzle (sometimes referred to as the Census-Taker Problem [1]) is a logical puzzle in number theory which on first inspection seems to have insufficient information to solve. However, with closer examination and persistence by the solver, the question reveals its hidden mathematical clues, especially when the solver ...
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...