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2
p+p^2+p^3+...+p^q=q+q^2+q^3+...q^p , p=q
p+p^2+p^3+...+p^q=q+q^2+q^3+...q^p , p=q
Source: Moldova TST 2021
September 19, 2021
number theory
prime numbers
Problem Statement
Prove that if
p
p
p
and
q
q
q
are two prime numbers, such that
p
+
p
2
+
p
3
+
.
.
.
+
p
q
=
q
+
q
2
+
q
3
+
.
.
.
+
q
p
,
p+p^2+p^3+...+p^q=q+q^2+q^3+...+q^p,
p
+
p
2
+
p
3
+
...
+
p
q
=
q
+
q
2
+
q
3
+
...
+
q
p
,
then
p
=
q
p=q
p
=
q
.
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