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Turkey Contests
Turkey Team Selection Test
2024 Turkey Team Selection Test
4
4
Part of
2024 Turkey Team Selection Test
Problems
(1)
A regular NT problem in Turkey TST
Source: 2024 Turkey TST P4
3/18/2024
Find all positive integer pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
such that,
1
0
a
!
−
3
b
+
1
2
a
\frac{10^{a!} - 3^b +1}{2^a}
2
a
1
0
a
!
−
3
b
+
1
is a perfect square.
number theory
modular arithmetic
Olympiad Number Theory
Perfect Squares
factorial