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If a is a square number or a = −1, then the density is 0, and if a is a perfect pth power for prime p, then the number needs to be multiplied by () (if there are more than one such prime p, then the number needs to be multiplied by () for all such primes p), and if a 0 is congruent to 1 mod 4, then the number needs to be multiplied by () for ...
The line is served by the 4, 5, 6, and <6> trains. The line was constructed in two main portions by the Interborough Rapid Transit Company (IRT), a private operator. The first portion, from City Hall north to 42nd Street, was opened between 1904 and 1908, and is part of the first subway line in the city .
Four northbound trips that terminated at Hunts Point Avenue between 3:53 and 5:05 p.m. were extended to Pelham Bay Park, reducing headways from nine to six minutes, and four northbound trips terminating at Third Avenue-138th Street between 3:36 and 4:48 p.m. were extended to Hunts Point Avenue, reducing headways from 4 + 1 ⁄ 2 to 3 minutes.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
The 125th Street station is an express station on the IRT Lexington Avenue Line of the New York City Subway.Located at Lexington Avenue and East 125th Street (also known as Dr. Martin Luther King Jr. Boulevard) in the East Harlem neighborhood of Manhattan, it is served by the 4 and 6 trains at all times, the 5 train at all times except late nights, and the <6> train during weekdays in peak ...
The 5 train always makes express stops, [168] and the 6 and <6> trains always make local stops; [167] the 4 train makes express stops during the day and local stops at night. [166] The next station northbound is 23rd Street for local trains and Grand Central–42nd Street for express trains, while the next station southbound is Astor Place for ...
In fact, if 2p divides n and p(p − 1) does not divide n, then p divides a n.) for every integer k (a condition is n + k(p − 1) must be > 1). For example, since 19 divides a 11 and 2 × 19 = 38 does not divide 11, so 19 divides a 18 k +11 for all k .