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2012 India Regional Mathematical Olympiad
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(2^x-1)(2^y-1)=2^{2^z}+1[Indian RMO 2012(b) Q3]
(2^x-1)(2^y-1)=2^{2^z}+1[Indian RMO 2012(b) Q3]
Source:
December 2, 2012
modular arithmetic
Problem Statement
Find all natural numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
such that
(
2
x
−
1
)
(
2
y
−
1
)
=
2
2
z
+
1.
(2^x-1)(2^y-1)=2^{2^z}+1.
(
2
x
−
1
)
(
2
y
−
1
)
=
2
2
z
+
1.
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