Recent content by whodsow

Media Man told me it is a generalization of Wilson's Theorem(http://mathworld.wolfram.com/WilsonsTheorem.html) Thanks.

Thank you, I've gotten the similar table. m phi rem 1 1 1 4 2 -1 6 2 -1 8 4 1 9 6 -1 10 4 -1 12 4 1 14 6 -1 15 8 1 16 8 1 18 6 -1 20 8 1 21 12 1 22 10 -1 24 8 1 25 20 -1 26 12 -1 27 18 -1 28 12 1 30 8 1 32 16 1 33 20 1 34 16 -1 35 24 1 36 12 1 38 18 -1 39 24 1 40...

Hi all, I had a problem, pls help me. Let b_1 < b_2 < \cdots < b_{\varphi(m)} be the integers between 1 and m that are relatively prime to m (including 1), of course, \varphi(m) is the number of integers between 1 and m that are relatively prime to m, and let B =...

well, thank your hint, I have proved that.

the Linear Equation Theorem says that the equation ax + by = gcd(a, b) always has a solution(s, u) in integers, and this solution can be found by the Euclidean algorithm, which we use to compute the gcd of a and b.

Why 4^{40n+k}\equiv4^{k}(mod\ 100)? this question is the same question as why the remainder of 2^{999} modulo 100 equals the remainder of 2^{999} modulo 25. let m = pq with gcd(p, q) = 1, then \phi(m)=\phi(p)*\phi(q), let a is divisible by p and not by q, then gcd(a, q) = 1, according to...

100 = 4 * 25, gcd(4, 25) = 1, so \phi(100)=40 and 4^{40n+k}\equiv4^{k}(mod 100). 2^{999}\equiv2*4^{499}\equiv2*4^{40*12+19}\equiv2*4^{19}\equiv2^{39}\equiv2^{10}2^{10}2^{10}2^{9}\equiv24*24*24*12\equiv88(mod 100)

I found a rule that the equation ax + by = (a-1)(b-1), for gcd(a, b)=1, has a solution in integers x and y with x ≥ 0 and y≥0, but the equation ax + by = (a-1)(b-1) - 1 don't. For example, the equation 3x + 7y = 12 has such soluntion (x, y) = (4, 0), but 3x + 7y = 11 has no such solutions that...

oh, thank you. I am a beginner, just starting to learn number theorem, I did not know this formulation until you told me.

thank your hint, CRGreathouse. I will try to prove it.

Hi. I have a question. I know the rule of the hightest power of 2 dividing n!, the highest power means if 2^{k}|n!, k is the greatest value. For example, n the hightest power of 2 dividing n! -------------------------------------- 1 0 2 1 3 1 4 3 5 3 6 4 7 4 8 7 9 7 10 8 11 8...