Solving $(m,n)$ for $m^2-2mn+14n^2=217$

Albert1 · Mar 15, 2017

$m^2-2mn+14n^2=217$
$m,n\in N$
find solution(s) of $(m,n)$

kaliprasad · Mar 15, 2017

Albert said:

$m^2-2mn+14n^2=217$
$m,n\in N$
find solution(s) of $(m,n)$

we have

$(m-n)^2 + 13n^2 = 217$
so $13n^2 < 127$ or $n^2 < 17 ( 13 * 17 = 221)$
trying n = 1,2,3,4,5 we get
n = 3 and m-n = 10 so m = 13 , n =3 is the solution and no other

Albert1 · Mar 16, 2017

kaliprasad said:

we have

$(m-n)^2 + 13n^3 = 217$
so $13n^2 < 127$ or $n^2 < 17 ( 13 * 17 = 221)$
trying n = 1,2,3,4,5 we get
n = 3 and m-n = 10 so m = 13 , n =3 is the solution and no other

sorry! have some others

kaliprasad · Mar 16, 2017

Albert said:

sorry! have some others

Yes I missed one more n=4, n-m = 3 giving m = 7, n= 4

Albert1 · Mar 16, 2017

kaliprasad said:

Yes I missed one more n=4, n-m = 3 giving m = 7, n= 4

still one missing

kaliprasad · Mar 16, 2017

Albert said:

still one missing

I should have taken |m-n| =3 giving m = 1 and n = 4

Solving $(m,n)$ for $m^2-2mn+14n^2=217$

Discussion

Undergrad Is infinity a necessary concept?

High School Ant on a stretchy rope puzzle

High School Potato paradox

Undergrad Descartes’ Geometry of Square Roots

High School Three Squares Problem

Mathematica NDSolve with forcing function via "digital waveguide"

MATLAB Unable to produce desired results using state-space model with observer for inverted pendulum

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Solving $(m,n)$ for $m^2-2mn+14n^2=217$

Discussion

Similar threads

Graduate Find All Pairs (m,n) with mn-1 Dividing n^3+1