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2015 Argentina National Olympiad
2
a+b and ab+1 are powers of 2
a+b and ab+1 are powers of 2
Source: 2015 Argentina OMA Finals L3 p2
January 16, 2023
number theory
power of 2
Problem Statement
Find all pairs of natural numbers
a
,
b
a,b
a
,
b
, with
a
≠
b
a\ne b
a
=
b
, such that
a
+
b
a+b
a
+
b
and
a
b
+
1
ab+1
ab
+
1
are powers of
2
2
2
.
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