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Switzerland - Final Round
2012 Switzerland - Final Round
4
4
Part of
2012 Switzerland - Final Round
Problems
(1)
no infinte sequance of primes with p_{k+1} = 2p_k - 1 or p_{k+1} = 2p_k + 1
Source: Switzerland - 2012 Swiss MO Final Round p4
12/30/2022
Show that there is no infinite sequence of primes
p
1
,
p
2
,
p
3
,
.
.
.
p_1, p_2, p_3, . . .
p
1
,
p
2
,
p
3
,
...
there any for each
k
k
k
:
p
k
+
1
=
2
p
k
−
1
p_{k+1} = 2p_k - 1
p
k
+
1
=
2
p
k
−
1
or
p
k
+
1
=
2
p
k
+
1
p_{k+1} = 2p_k + 1
p
k
+
1
=
2
p
k
+
1
is fulfilled. Note that not the same formula for every
k
k
k
.
number theory
prime
primes
recurrence relation