不自然
发表于 2025-3-25 03:41:13
Primesds counter-intuitive and, in fact, it isn’t true, as Euclid demonstrated a long time ago. Actually, he did it without demonstrating any primes — he just showed that assuming a finite number of primes leads to a neat contradiction.
CRAB
发表于 2025-3-25 10:01:11
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建筑师
发表于 2025-3-25 12:27:03
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Modify
发表于 2025-3-25 18:21:20
Linear Congruences, flying the same route, is only 2 to 3 hours late. If you were in a hurry, which airline would you fly — food, lack of leg room and all else being equal? Obviously, being 25 hours late is as good (or bad) as being only 1 hour late. In other words, in a . event an extra day, or even several, makes n
玩忽职守
发表于 2025-3-25 22:35:53
Diophantine Equations Early historical occurrences often appeared in the guise of ., and perhaps for that reason, Diophantine equations have been largely neglected in our mathematical schooling. Ironically, though, Diophantine equations play an ever-increasing role in modern applications, not to mention the fact that so
金桌活画面
发表于 2025-3-26 02:29:15
The Theorems of Fermat, Wilson and Eulerry of groups, and indeed, their most elegant proofs are group theoretic. Here, however, we shall stress the purely arithmetic viewpoint. We also introduce the important . (or totient function) which reaches into every corner of number theory and which, by way of illustration, tells us how many ways
Serenity
发表于 2025-3-26 07:03:17
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COM
发表于 2025-3-26 11:22:40
The Prime Divisor Functionsare there?” Some of the answers will be rather counterintuitive. Thus, a 50-digit number (10. times the age of our universe measured in picoseconds) has only about 5 different prime factors on average and even more surprisingly — 50-digit numbers have typically fewer than 6 prime factors in all, eve
Proclaim
发表于 2025-3-26 15:13:44
Certified Signaturesse of avoiding random confusions) achievable by this method, which is based on modular arithmetic, appears to exceed by far that of notarized signatures, fingerprinting or, conceivably, even genetic analysis.
议程
发表于 2025-3-26 20:28:21
Primitive Roots helped the young Gauss to reduce the equation .. + .. + ... + . + 1 = 0 to several quadratic equations leading to the construction of the regular 17-gon. These same concepts also allow us to see why the decimal fraction of 1/7 has a period of length 6, while the decimal fraction for 1/11 has a peri