Recent content by beetle2

((n-1)*(n+1)*(n^2+1)=0 mod 3 when n = 2 ((n-1)*(n+1)*(n^2+1)=0 mod 3 when n = 1 ((n-1)*(n+1)*(n^2+1)*(n^4+1)*(n^8+1)*(n^16+1)) = 0 mod 5 when n = 1 ((n-1)*(n+1)*(n^2+1)*(n^4+1)*(n^8+1)*(n^16+1)) = 0 mod 5 when n = 2 ((n-1)*(n+1)*(n^2+1)*(n^4+1)*(n^8+1)*(n^16+1)) = 0 mod 5 when n...

These are the factors. (x - 1) x (x + 1) (x2 + 1) (x4 + 1) (x8 + 1) (x16 + 1) Do i have to reduce these to irreducible polynomials mod 15 ?

Homework Statement Show that for every integer n the number n33 - n is divisible by 15 Homework Equations The Attempt at a Solution Not sure what to do. I was thinking it might have something to do with both numbers are divisable by 3 ie the power = 3 x 11 and the divisor...

thankyou very much for the explanation micromass much appreciated

I'm not sure. I checked then answers in the book and it has (142)(5876) not sure how they got it as theirs dosn't have a (3)?

Homework Statement Express the element in matrix A= 1,2,3,4,5,6,7,8 4,1,3,2,8,5,6,7 of s8 as a product disjoint cycles [b]2. Homework Equations [/b The Attempt at a Solution I pick a number say the first 1 and pu it in parenthises. (1, I multiply by the number in th...

Homework Statement Rewrite the 2nd oder non linear D.E \frac{d^2x}{dt^2}+x^2+x=0 as a series of 1st order equations Homework Equations a\frac{d^2x}{dt^2}+b\frac{dx}{dt}+cx=0 \frac{dx}{dt}=y \frac{dy}{dt}=-\frac{c}{a}x-\frac{b}{a}y The Attempt at a Solution a=1, b=0 , c=1...

Hi guys, Can someone please explain how you find the eigenvalues of this type? u''+\lambda u =0 or point me to some decent literature? regards Brendan

I think I need some more practice, It can get confusing just doing ordinary polynomial division without having modulo as well x^3+2x+3 thanks for your help

I multiply it out and get x^3-13x-12 which is x^3-3x-2mod 5 so I'm doing something wrong.

Is there a way to check that my answer is right?

I evaluated x+1 \div x^2-3x+1 which is P(X)= x-4 zero remainder mod 5 So I have three irreducible Polynomials whose degrees add to three ie (x+3)(x+1)(x-4) Hows that look

Homework Statement Write P(x) = x^3+2x+3 as the product of Irreducible Polynomials over Z_5 Homework Equations Polynomial division The Attempt at a Solution I start out by taking out a factor of x+3 That is x+3 \div x^3+2x+3 I get P(x) = x^2-3x+1 which has zero...

Hi guys, I know that for integral domains with finte elements that if we show that each element has a multiplicative inverse then it is a field. I need to show that the field of fractions is a field. As the domain is not finite how does that effect the proof of being a field...

Do I have to try to combine the first functions and set the right side to = 0 ? My examples in my notes are all of the form \alpha^2\frac{F''}{F}=\frac{ G'}{G}