Show that there are no solutions to the equation p2 + q2 = r2 + s2...

Question

Question

Show that there are no solutions to the equation p² + q² = r² + s² + t² where p, q, r, s, t are primes.

Answer 1

Answer #1

- these is I 2 or وه ره Anso p²+q² 82 +8² +² 8+²+t² is divisible by 8. we first show that 8248²7t² Since its equiraket to sho

Answer 2

Similar Homework Help Questions

Show that there are no solutions to the equation p+ q2 = y2 + y2 +...

Show that there are no solutions to the equation p+ q2 = y2 + y2 + t2 where p, q, r, s, t are primes. (Hint: Consider the remainder of the square of an odd integer when divided by 8, and then consider cases.]
Bonus (Abel's formula) a) Show that if y1 and y2 are solutions to the differential equation...

Bonus (Abel's formula) a) Show that if y1 and y2 are solutions to the differential equation y"p(t)y(t)y 0 where p and q are continuous on an interval I, then the Wronskian of y and y2, W(y1,y2) (t) is given by - Sp(t)dt ce W(y1, y2)(t) where c depends on y and y2 (b) Use Abel's formula to find the Wronskian of two solutions to the differential equation ty"(t 1)y 3y 0 Do not solve the differential equation
If a(alpha)= n, some of their solutions are polynomial. Show that p(t)=dˆn/dtˆn (tˆ2 - 1)ˆn is a solution by the follow equation Legendre Polynomials ) =ア 교흙(t2-1)" son conocidos corno los pol...

If a(alpha)= n, some of their solutions are polynomial. Show that p(t)=dˆn/dtˆn (tˆ2 - 1)ˆn is a solution by the follow equation Legendre Polynomials ) =ア 교흙(t2-1)" son conocidos corno los polinomios de (d) Los polinomios P(t Legendre. Calcule los primeros cuatro polinomios P, P2, Ps, Ps ) =ア 교흙(t2-1)" son conocidos corno los polinomios de (d) Los polinomios P(t Legendre. Calcule los primeros cuatro polinomios P, P2, Ps, Ps

598) Refer to Figure 592. [R1,C1,S1,P1 ]- [16,13,0,1 [R2,C2,S2,P2]1 7, 8,1,0]. Determine ans:6 A,...

598) Refer to Figure 592. [R1,C1,S1,P1 ]- [16,13,0,1 [R2,C2,S2,P2]1 7, 8,1,0]. Determine ans:6 A,B,C, D, E,F. Figure 592 Z2 Z1 V1 (s) V2(s) R R1 I R2 or not present V2(s) DsEsF V1 (s) DsEsV2(s) V1 (s) AsBs C As +BsC A zero or one B& C- one [R1,C1,S1,P1]-[ohms, farads, series, parallel for Z1 R2,C2,S2,P2]-[ohms, farads, series, parallel] for Z2 zero means NO or NOT PRESENT or DOES NOT APPLY series or parallel- one means series or parallel combination if...
2. Show that if are analytical functions in an environment of the point y so the equation solutions: they are al...

2. Show that if are analytical functions in an environment of the point y so the equation solutions: they are also analytical functions in a certain environment of the same point, what form do the solutions have? P(), Q), R(x) We were unable to transcribe this imageP(x0 P Qy (x)R()y(x) 0 P(), Q), R(x) P(x0 P Qy (x)R()y(x) 0
Consider the differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation...

Consider the differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation above. T1,T2 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. n(t) = v2(t) (c) Find a particular solution yp of the differential equation above. Bplt)

h Bessel equation of order p is ty" + ty + (t? - p2 y =...

h Bessel equation of order p is ty" + ty + (t? - p2 y = 0. In this problem assume that p= 2. a) Show that y1 = sint/Vt and y2 = cost/vt are linearly independent solutions for 0 <t<o. b) Use the result from part (a), and the preamble in Exercise 3, to find the general solution of ty" + ty' + (t2 - 1/4)y = 3/2 cost. (o if 0 <t < 12, y(t) = { 2...
(2) Let T: P2 + R2 be given by T(p) = [pc] (e.g. if p= a...

(2) Let T: P2 + R2 be given by T(p) = [pc] (e.g. if p= a + bx, then p(4) = a + b(4) = a + 4b.) (a) Find the matrix of T relative to the standard bases B = {1, 2,2} of P2, and C = {ej,ez} of R (b) Find the matrix of T relative to the basis A = {1, 1+,1+x+x?} of P2 and D= {(1, 1), (1, -1)} of R2 (c) Find a basis for...
Let T : P2 → R2 be given by T(p) = p(1) +p(-1) p(2) Suppose that...

Let T : P2 → R2 be given by T(p) = p(1) +p(-1) p(2) Suppose that qe ker(T) is not 0. Find the roots of q.

Consider a linear space P2(R) with the standard basis S- {1,t,t, t 3). a. Describe the...

Consider a linear space P2(R) with the standard basis S- {1,t,t, t 3). a. Describe the isomorphism P R sending p(t) ps b. Show that B [t - 1,t + 1,t2 +t, t3) is another basis for P3 (R). c. Let p(t) 32t4t3. Find p. d. Show that the map P R4 sending p(t)-, рв is an isomorphism.