Recent content by yeland404

Homework Statement The problem of minimizing f(x1, x2) = x1^3 subject to (x1 + 1)^3 = (x2 − 2)^2 is known to have a unique global solution. Use the method of Lagrange multipliers to find it. You should deal with the issue of whether a constraint qualification holds. Homework Equations...

I need to prove that a be a odd integer that congruence X^2\equiva mod 2 is always solvable with exactly one incongruent solution modulo 2. this question is linked with (b) let a be an odd integer. Prove that the congruence X^2\equiva mod 4 is solvable iff a\equiv1 mod 4. in this case ,prove...

number theory -- quadratic residues Homework Statement find all incongruent solutions of each quadratic congruence below. X^2\equiv23 mod 77 Homework Equations X^2\equiv11 mod 39 The Attempt at a Solution it is suffices to X^2\equiv23 mod 7, andX^2\equiv23 mod 11, then how to do next?

number theorm -- Euler theorem Homework Statement let be an integer that not divisible by 3. Prove that n^7\equivn mod 63 Homework Equations none The Attempt at a Solution it is suffice to prove that n^7\equivn mod 7,n^7\equivn mod 9, i get n^7\equivn mod 7 by Euler theorem ...

Homework Statement let a and b be integers that not divisible by the prime number p if a^p\equivb^p, prove that a^p\equivb^p mod p^2 Homework Equations if a^p\equivb^p, prove that a\equivb mod p The Attempt at a Solution I already get that a\equivb mod p , then how can I get...

then n^21-n = n(n^20-1), suppose n is even , then 2|n^21-n if n is odd, n^20 is odd, so n^20-1 is even; to 3, it means n^21=(n^3）^7=n^7=(n^3)^2*n then how is the next to prove 3|n(n^20-1)

Homework Statement let n be an integer . Prove the congruence below. n^21 \equiv n mod 30 Homework Equations n^7 \equiv n mod 42 n^13 \equiv n mod 2730 The Attempt at a Solution to prove 30| n^21-n，it suffices to show 2|n^21-n,3|n^21-n,5|n^21-n and how to prove them?

Homework Statement Prove that n ℂ Z+ is divisible by 3( respectively 9). to show that if and only if the sum of its digits is divisible by 3 Homework Equations The Attempt at a Solution so n= 3q, q>3 that n\equiv0 mod 3 n=X1* 10^n+ x2*10^n-1...Xn so need to...

Homework Statement a,b,c belong to Z with (a,b)=1. Prove that if a|c and b|c, then ab|c Homework Equations let a1,a2...an, c belong to Zwith a1...an pairwise relatively prime, prove if ai|c for each i, then a1a2...an|c The Attempt at a Solution if a|c, then c=ea, b|c, then c=fb...

Homework Statement prove or disprove the following conjecture: If n is a positive integar, then n^2 - n +41 is a prime number Homework Equations no, just prove or disprove The Attempt at a Solution I think one possible answer may be there is no factorization for this except...

I know how to do with the X'=AX that x=c1e^λt[u1]...however, what I get is a single equation. I have no idea how to deal with five variables...

How to deal with homogenous differential equation system?? Homework Statement s'[t] == (-3 s[t])/580, m'[t] == (-19 m[t])/590, h'[t] == (3 s[t])/580 + (19 m[t])/590 - (2 h[t])/25, e'[t] == (2 h[t])/25 - (85 e[t])/116, o'[t] == (85 e[t])/116 - (33 o[t])/131 Homework Equations it...

so Ker (A^2)=0 can lead to Ker(A^4)=0,then?

so times A on both side of the equation?

vector w belons to the image of matrix A, and the image of linear transformation Ax is the span of the column vector in A