Hi everybody,
We define multiplication as an operation with these properties :
a(b+c)=ab+ac and (a+b)c=ac+bc ,a*0=0 and a*1=a with a,b,c natural numbers and of course the two properties Zurtex mentioned ab=ba and a(bc)=(ab)c-I "forgot" to mention them because I didn't use them in what is...
Hey!
Can someone please give me a hint on this :rolleyes:
Prove:
\sum_{n=1}^n i^4 = \frac{n(n+1)(2n+1)(3n^2 + 3n - 1)}{30}
What I've got so far:
Let P(n) be the statement:
\sum_{n=1}^n i^4 = \frac{n(n+1)(2n+1)(3n^2 + 3n - 1)}{30}
Let n=1 we get;
\sum_{n=1}^1 i^4 =...
Primes in ring of Gauss integers - help!
I'm having a very difficult time solving this question, please help!
So I'm dealing with the ring R=\field{Z}[\zeta] where
\zeta=\frac{1}{2}(-1+\sqrt{-3})
is a cube root of 1.
Then the question is:
Show the polynomial x^2+x+1 has a root in F_p if...
We have a question that asks to find the number of integers between 1 and 100 that are divisible by 2,3 or 5.
So i use the sum rule
let E,F and G be the the integers. so,
n(EUFUG) = n(E) + n(F) + n(G) - n(EnF) - n(EnG) - n(FnG)
but this doesn't work. it gives me the answer of 70 but the...
Let a, b, c and d be 4 distinct integers. Find the smallest possible value for 4(a^2 + b^2 + c^2 + d^2) - (a+b+c+d)^2 and prove that your answer is correct.
I got 20 as the smallest answer. Thats when u have a, b, c, and d as 4 consective integers, but i can't prove my answer. Can anyone...
I have to either give an example or show that no such function exists:
A real valued function f(x) continuous at all irrationals and at all the
integers, but discontinuous everywhere else.
I think such function exists and I would define it as follows:
f(x) = 0 if x is an irrational...
Ok, I haven't done maths for a few years now and I've been set the following question:
The sum of the first integers is given by:
Sum(n) = 1+2+3+4 ... +n = n(n+1)/2
Find similar formulae for
Even(n) = 2+4+6+8 ... +2n
Odd(n) = 1+3+5+7 ... +(2n-1)
Now the formulae I have come...
hi i am new to THIS place here but i do put posts on the number theory site as well. i am in need of direction and have no idea where to turn. i need help w/ two ?'s and they are...
how many pos int. <1000 are NOT divisible by 12 or 15?
prove the if the sum of two consec. int. is a...
Problem: Write the number 3.1415999999999... as a ratio of two integers.
In my book, they have a similar example, but using 2.3171717... And this is how they solved that problem.
2.3171717... = 2.3 + (17/10^3) + (17/10^5) + (17/10^7) + ...
After the first term we have a geometric series...
The arithmetic mean of a set of nine different positive integers is 123456789. Each number in the set contains a different number of digits with the greatest value being a nine-digit number. Find the value of each of the nine numbers .
Induction Hypothesis:
In fact pa is true for all integers n greater than a particular base value and you should complete the proof given below to use the principle of mathematical induction to prove this.
pa : n-2 < (n^2 – 3n)/12
Base case is n = 14
Because: n-2 < (n^2 – 3n)/12...