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don't understand it at all
I can only prove that
Think harder! the solution will be obvious when you draw the graph
In Z17, 5^2>17 , therefore the solutions exist only above or equal to 5. Let X be the solution ,
solve this one .Oh...I forgot how to solve this equation....I am sure it can be solved.Nobody?? Really urgent~
The following formula comes from Graduate Text ,Elementary Number Theory by Melvyn B.Nathanson
For any nonzero integer n and prime number p, we define
as the greatest integer r such that divides n.For every positive integer n and prime p
Example : 10!
Oh , I know now.
0 1 2 3 4 5 6 7 8 9 10 ........n
0 0 0 0 0 0 0 0 0 0 0 0 ........0
1 0 1 2 3 4 5 6 7 8 9 10.........n
2 .........................................
Yeah, but can't it be solved by Modulo method?
simplified ,get
Looks very symmetric~lol
cosa=cosb=cosc=1/2 my first impression. lol
Construct the multiplication table for the ring
.What's multi table? My textbook doesnt tell~
yeah , I know I need to prove this one , but I can't crack it. I think maybe using the Pythagoras number generating forumla will work?
,oh , it won't work either...gotta find a way aroundI am so stupid , I have no clue,help me out
No.2 11:8 right?
I practice Counter Strike in my spare time , anyone want to team up and fight for glory? lol
8th grader ,welcome!
I am in San Francisco now
When is 1+x^1+x^2+x^3........x^m=y^n for x,y,m,n>=3
for example 1+3+3^2+...3^4=11^2
I try everything I can think of , stilll hehe
Oh , right , just use modula to show can't all be primes .
Another question how to construct muplication table for ring ?
First , I can solve half of the section , As, I learn more and more I can solve fewer and fewer problems...Help!
Here another two
7.Let 2=p(1)<p(2)<.... be the sequence of primes in increasing order Prove that p(n)<=2^2^(n-1) for all n>=1
8.Let a and b be positive integers with a>b . The length of the Euclidean algorithm for a and b, denoted by E(a,b) , is the number of divisions required to find the greatest common divisor of a and b . Prove that E(a,b)<= (logb/log@)+1 , where @= (1+5^1/2)/2 [I think this one is the hardest ]
How to type those math code? I mean it displayed like....uh..cool
1.Find all solutions of the Ramanujan-Nagell diophantine equation x^2+7=2^n with x<=1000
2.Find all solutions of the Ljunggren diophantine equation x^2 - 2y^4=-1
3.For n>=1 consider the rational number, h(n)=1+1/2+1/3+......+1/n
Prove that h(n) is not an integer for any x>=2
4.Prove that n, n+2, n+4 are all primes if and only if n=3.
5.The prime numbers p and q are called twin primes if |p-q|=2, Prove that if p and q are twin primes greater than 3 then q+p is divisible by 12
6.Prove that if x,y,z are integer such that x^2+y^2=z^2 , then xyz=0(mod 60) [note that = is modula =]
This text book Elementary Methods in Number Theory is madness , some exercises even require you to prove theorems that put forward by Mathematician.Anyone read it ?written by Melvyn B.Nathanson.