Recent content by ripcity4545

thanks to both!

Homework Statement Prove that Z sub n is cyclic. (I can't find the subscript, but it should be the set of all integers, subscript n.)Homework EquationsLet (G,*) be a group. A group G is cyclic if there exists an element x in G such that G = {(x^n); n exists in Z.} (Z is the set of all...

nope, that doesn't work. I am definitely stuck on proving that a base k palindromic number with even digits is divisible by k+1.

thank you. and for a base k palindromic number, can I just substitute k for 10?

thanks for your help.

Okay, thanks. I think I figured it out in base 10 by proving that you can factor out (10^p +1) from each term, where p is some odd power, and then I proved by induction that 10^(2n-1) +1 is divisible by 11. Any ideas on the general base n case? I can see that it works, just by using...

Well if we are considering divisibility by 5, i can let m=5k+r, where k is some integer and r may be 0, 1, 2, 3, or 4. So m^2 = 25k^2 + 10kr +r^2 so m^2 ≡ n mod 5 equals: 25k^2 + 10kr +r^2 ≡ n mod 5 and since 25k^2 + 10kr ≡ 0 mod 5, we are left with r^2 ≡ n mod 5 so n...

Homework Statement If 5 divides m^2 + n^2 + p^2 , prove that 5 divides wither m, or n, or p. Homework Equations m,n,p are all integers The Attempt at a Solution I am having some major problems with this chapter on modular arithmetic. any help is much appreciated! modular arithmetic is...

Homework Statement Prove that every palindromic integer N in base 10 with an even number of digits is divisible by 11. Then prove that every palindromic integer in base k with an even number of digits is divisible by k+1. Homework Equations palindromic means the number reads the...

For N>0, I can't think of any N that cannot be defined by ab(b+1)/2. My problem is proving it. I tried induction but that leaves me with P(k): ak(k+1)/2= N and P(k+1): a(k+1)((k+1)+1)/2= N = ak(k+1)/2 + k+1 =N. Thanks for your help so far.

This helped a lot for me on the induction concept: http ://en. wikipedia. org/wiki/Mathematical_induction

Sorry i forgot- 0 is not included in naturals in this case. but using your help, I got: since the codomain is N, we can let f(a,b) = 1. However, there are no a,b in N that satisfy a+b=1, so the function is not surjective. Now I cannot find any counterexample of the second equation...

1? I'm still not clear what f(a, b) means.

for a function A-->B, (A is the domain and B is the range), a funtion is surjective if for each b in B, there is at least one x in A such that f(x)=b.

Homework Statement The problem is : For the functions from N*N --> N, determine if the following functions are surjective: f(a, b) = a + b f(a, b) = ab(b+1)/2 Homework Equations N is all natural numbers The Attempt at a Solution My problem is I know the definition of...