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National and Regional Contests
Finland Contests
Finnish National High School Mathematics Competition
2016 Finnish National High School Mathematics Comp
4
4
Part of
2016 Finnish National High School Mathematics Comp
Problems
(1)
diophantine (4a-b)(4b-a )=1770^n
Source: Finland 2016, p4
9/8/2019
How many pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of positive integers
a
,
b
a,b
a
,
b
solutions of the equation
(
4
a
−
b
)
(
4
b
−
a
)
=
177
0
n
(4a-b)(4b-a )=1770^n
(
4
a
−
b
)
(
4
b
−
a
)
=
177
0
n
exist , if
n
n
n
is a positive integer?
number theory
Diophantine equation
diophantine