MathDB

diophantine equation involving reciprocals of squares

Source: France 1990 P3

May 18, 2021

number theoryDiophantine equation

Problem Statement

(a) Find all triples of integers

(a,b,c)

for which

\frac14=\frac1{a^2}+\frac1{b^2}+\frac1{c^2}

. (b) Determine all positive integers

n

for which there exist positive integers

x_1,x_2,\ldots,x_n

such that

1=\frac1{x_1^2}+\frac1{x_2^2}+\ldots+\frac1{x_n^2}