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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 ...
However, the linear congruence 4x ≡ 6 (mod 10) has two solutions, namely, x = 4 and x = 9. The gcd(4, 10) = 2 and 2 does not divide 5, but does divide 6. Since gcd(3, 10) = 1, the linear congruence 3x ≡ 1 (mod 10) will have solutions, that is, modular multiplicative inverses of 3 modulo 10 will exist. In fact, 7 satisfies this congruence (i ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random prime in same range. Prime Numbers List Full list for prime numbers below 10,000,000,000, partial list for up to 400 digits.
Brand Name Banquet. Recipes from brand name companies often get a bad rap. But many people learned to cook from the backs of boxes, bottles, and jars, especially in the 1950s, 60s, and 70s when ...
Drake's Cake – He's Got a Cake For Heaven's Sake – A strip about Sir Francis Drake trying to protect a cake. Driving David Beckham or Driving Mister David – a spoof of Beezer and (later) Beano comic strip " The Numskulls " in which we see the inner thought processes – or lack thereof – of David Beckham .
John Selfridge has conjectured that if p is an odd number, and p ≡ ±2 (mod 5), then p will be prime if both of the following hold: 2 p−1 ≡ 1 (mod p), f p+1 ≡ 0 (mod p), where f k is the k-th Fibonacci number. The first condition is the Fermat primality test using base 2.