Question
In: Advanced Math
Show that every Pythagorean triple (x, y, z) with x, y, z having no common factor...
Show that every Pythagorean triple (x, y, z) with x, y, z having no common factor d > 1 is of the form (r^2 - s^2, 2rs, r^2 + s^2) for positive integers r > s having no common factor > 1; that is
x = r^2 - s^2, y = 2rs, z = r^2 + s^2.
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Show that if (x,y,z) is a primitive Pythagorean triple, then X and Y cannot both be...
Show that if (x,y,z) is a primitive Pythagorean triple, then X and
Y cannot both be even and cannot both be odd. Hint: for the odd
case, assume that there exists a primitive Pythagorean triple with
X and Y both odd. Then use the proposition "A perfect square always
leaves a remainder r=0 or r=1 when divided by 4." to produce a
contradiction.
If (x,y,z) is a primitive Pythagorean triple, prove that z= 4k+1
If (x,y,z) is a primitive Pythagorean triple, prove that z=
4k+1
Let x, y, z be a primitive Pythagorean triple with y even. Prove that x+y ≡...
Let x, y, z be a primitive Pythagorean triple with y even. Prove
that x+y ≡ x−y ≡ ±1 mod 8.
A Pythagorean triplet is a set of positive integers (x, y, z) such that x2 +...
A Pythagorean triplet is a set of positive integers (x, y, z)
such that x2 + y2 = z2. Write an interactive script that asks the
user for three positive integers (x, y, z, in that order). If the
three numbers form a Pythagorean triplet the script should a)
display the message ‘The three numbers x, y, z, form a Pythagorean
triplet’ b) plot the corresponding triangle using red lines
connecting the triangle edges. Hint: place the x value on...
Suppose x,y ∈ R and assume that x < y. Show that for all z ∈...
Suppose x,y ∈ R and assume that x < y. Show that for all z
∈ (x,y), there exists α ∈ (0,1) so that αx+(1−α)y = z. Now, also
prove that a set X ⊆ R is convex if and only if the set X satisfies
the property that for all x,y ∈ X, with x < y, for all z ∈
(x,y), z ∈ X.
Use spherical coordinates to evaluate the triple integral ∭e^−(x^2+y^2+z^2)/(x^2 + y^2 + z^2) dV , Where...
Use spherical coordinates to evaluate the triple integral
∭e^−(x^2+y^2+z^2)/(x^2 + y^2 + z^2) dV , Where E is the region
bounded by the spheres x^2 + y^2 + z^2 = 4 and x^2 + y^2 + z^2 =
9
The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just...
The curried version of let f (x,y,z) = (x,(y,z)) is
let f (x,(y,z)) = (x,(y,z))
Just f (because f is already curried)
let f x y z = (x,(y,z))
let f x y z = x (y z)
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}.
a) Prove or disprove: A ⊆ X
b) Prove or disprove: X ⊆ A
c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y )
d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )
If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z)...
If X, Y and Z are three arbitrary vectors, prove these
identities:
a. (X×Y).Z = X.(Y×Z)
b. X×(Y×Z) = (X.Z)Y – (X.Y)Z
c. X.(Y×Z) = -Y.(X×Z)
Set up the triple integral of an arbitrary continuous function f(x, y, z) in spherical coordinates...
Set up the triple integral of an arbitrary continuous function
f(x, y, z) in spherical coordinates over the solid shown. (Assume a
= 4 and b = 8. ) f(x, y, z) dV E = 0 π/2 f , , dρ dθ dφ 4
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- PUT IN JAVA PROGRAMMING The StockB class: Design a class named StockB that contains the following...
- Draw a DFA for the following ( ∑ = {0,1}): Set of all strings with.
- In the article from Forbes notes that the goal of a leader is not to clone...
- Many people keep time using a 24 hour clock (11 is 11am and 23 is 11pm,...
- UNIX ONLY -- DIFFICULT LAB ASSIGNMENT This is an extremely difficult subject for me. Could you...
- Do you know why your credit card can be refused even though you are profitable?
- The Following Java expression: S/10 * 10 + 10 – S = C Show that this...
ADVERTISEMENT