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Regional Mathematical Olympiad
2013 India Regional Mathematical Olympiad
1
Indian RMO- Paper 2
Indian RMO- Paper 2
Source: Problem 1
December 11, 2013
modular arithmetic
number theory unsolved
number theory
Problem Statement
Prove that there do not exist natural numbers
x
x
x
and
y
y
y
with
x
>
1
x>1
x
>
1
such that ,
x
7
−
1
x
−
1
=
y
5
+
1
\frac{x^7-1}{x-1}=y^5+1
x
−
1
x
7
−
1
=
y
5
+
1
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