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Mexico National Olympiad
2013 Mexico National Olympiad
1
1
Part of
2013 Mexico National Olympiad
Problems
(1)
Primes dividing their indices
Source: Mexican Mathematical Olympiad 2013 Problem 1
12/1/2013
All the prime numbers are written in order,
p
1
=
2
,
p
2
=
3
,
p
3
=
5
,
.
.
.
p_1 = 2, p_2 = 3, p_3 = 5, ...
p
1
=
2
,
p
2
=
3
,
p
3
=
5
,
...
Find all pairs of positive integers
a
a
a
and
b
b
b
with
a
−
b
≥
2
a - b \geq 2
a
−
b
≥
2
, such that
p
a
−
p
b
p_a - p_b
p
a
−
p
b
divides
2
(
a
−
b
)
2(a-b)
2
(
a
−
b
)
.
inequalities
number theory
prime numbers
number theory proposed