I am not able to find any such triple, only find infinitely many triples with one of it is a perfect power.
2026-03-26 22:53:37.1774565617
Does there exist a primitive pythagorean triple $(a, b, c)$ with $a$ and $b$ are perfect powers (bigger than one)?
124 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ELEMENTARY-NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- How do I show that if $\boldsymbol{a_1 a_2 a_3\cdots a_n \mid k}$ then each variable divides $\boldsymbol k $?
- Using only the digits 2,3,9, how many six-digit numbers can be formed which are divisible by 6?
- Algebra Proof including relative primes.
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
- algebraic integers of $x^4 -10x^2 +1$
- What exactly is the definition of Carmichael numbers?
- Number of divisors 888,888.
Related Questions in PYTHAGOREAN-TRIPLES
- Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
- Can we find $n$ Pythagorean triples with a common leg for any $n$?
- Is there a Pythagorean triple whose angles are 90, 45, and 45 degrees?
- Radius of Circumcircle formed by triangle made of Pythagorean triplet
- How many variations of new primitive Pythagorean triples are there when the hypotenuse is multiplied by a prime?
- Pythagorean Type Equation
- Baffling Pythagoras Theorem Question
- $3$ primitive pythagorean triples from 6 integers.
- Infinitely many integer triples $(x, y, z)$ satisfying $x^2 + 2y^2 = 3z^2$
- Proof By Descent FLT
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
A multiple of 3,4,5 gives: 27,36,45.
That is, $(3^3)^2+(6^2)^2=45^2$.
In some generality, if you have a Pythagorean triple $(a,b,c)$ where $b=d^\ell$, then $(a^{\ell+1}, (ad)^\ell, c\cdot a^\ell)$ seems to be a triple of the form you want.