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Soros Olympiad in Mathematics
I Soros Olympiad 1994-95 (Rus + Ukr)
9.5
1/p +q/(q^r -1)=1 (I Soros Olympiad 1994-95 R1 9.5 10.3)
1/p +q/(q^r -1)=1 (I Soros Olympiad 1994-95 R1 9.5 10.3)
Source:
July 30, 2021
number theory
Diophantine equation
diophantine
Problem Statement
Find the triplets of natural numbers
(
p
,
q
,
r
)
(p,q,r)
(
p
,
q
,
r
)
that satisfy the equality
1
p
+
q
q
r
−
1
=
1.
\frac{1}{p}+\frac{q}{q^r -1}=1.
p
1
+
q
r
−
1
q
=
1.
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