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National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
1966 Dutch Mathematical Olympiad
2
2
Part of
1966 Dutch Mathematical Olympiad
Problems
(1)
t_{n+1} = 2(t_n)^2 - 1, gcd (t_n,t_m) = 1
Source: Netherlands - Dutch NMO 1966 p2
1/31/2023
For all
n
n
n
,
t
n
+
1
=
2
(
t
n
)
2
−
1
t_{n+1} = 2(t_n)^2 - 1
t
n
+
1
=
2
(
t
n
)
2
−
1
. Prove that gcd
(
t
n
,
t
m
)
=
1
(t_n,t_m) = 1
(
t
n
,
t
m
)
=
1
if
n
≠
m
n \ne m
n
=
m
.
number theory
greatest common divisor
GCD
recurrence relation