Sum of Squares 1

Number Theory Level 3

$a$ , $b$ , $c$ , $d$ , $e$ , $f$ , and $g$ are all distinct, positive integers such that $a^2 + b^2 = c^2 + d^2 = e^2 + f^2 = g$ .

What is the smallest possible value of $g$ ?

4 solutions

Kyle T
Apr 3, 2019

I wrote some code to brute force it
Probably not the most elegant solution but it works

OK so

that php site is way more powerful than ka cs

that or the last 2 variables make an exponential difference

see my comment on the persons solution for https://brilliant.org/problems/sum-of-squares-2-2/

my codes there

chase marangu - 2 years, 2 months ago

Joshua Lowrance
Mar 2, 2019

$325=18^2+1^2=17^2+6^2=15^2+10^2$ .

I leave the challenge to the solver to prove that this is the smallest :)

Chase Marangu
Nov 15, 2019

X X
Mar 3, 2019

I tried $g=(1^2+2^2)(1^2+2^2)(2^2+3^2)$ and worked!

that doesnt make sense

chase marangu - 2 years, 2 months ago

here you have a=1, b=2, c=1, d=2, e=2, f=3
OP said every letter is distinct, therefore this wouldnt fit

Kyle T - 2 years, 2 months ago

oh i see he said he tried 1 2 1 2 2 3 as a b c d e f respectively i thought he was just, spontaneously spamming some arbitrary mathematical syntax

chase marangu - 2 years, 2 months ago