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5
Exponential Equation
Exponential Equation
Source: 2011 IrMO Paper 2 Problem 5
February 8, 2018
number theory
Problem Statement
Find with proof all solutions in nonnegative integers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
of the equation
1
1
a
5
b
ā
3
c
2
d
=
1
11^a5^b-3^c2^d=1
1
1
a
5
b
ā
3
c
2
d
=
1
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