MathDB

1/x+1/y=1/n

Source: Argentina 1995 OMA L3 p2

May 13, 2024

number theoryDiophantine equationdiophantine

Problem Statement

For each positive integer

n

let

p(n)

be the number of ordered pairs

(x,y)

of positive integers such that

\dfrac{1}{x}+\dfrac{1}{y} =\dfrac{1}{n}.

For example, for

n=2

the pairs are

(3,6),(4,4),(6,3)

. Therefore

p(2)=3

. a) Determine

p(n)

for all

n

and calculate

p(1995)

. b) Determine all pairs

n

such that

p(n)=3

.

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