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Serbia National Math Olympiad
2022 Serbia National Math Olympiad
P6
P6
Part of
2022 Serbia National Math Olympiad
Problems
(1)
Algebra with primes
Source: Serbian national olympiad 2022 P6
4/8/2022
Let
p
p
p
and
q
q
q
be different primes, and
α
∈
(
0
,
3
)
\alpha\in (0, 3)
α
∈
(
0
,
3
)
a real number. Prove that in sequence
[
α
]
,
[
2
α
]
,
[
3
α
]
…
\left[ \alpha \right] , \left[ 2\alpha \right] , \left[ 3\alpha \right] \dots
[
α
]
,
[
2
α
]
,
[
3
α
]
…
exists number less than
2
p
q
2pq
2
pq
, divisible by
p
p
p
or
q
q
q
.
algebra
primes
Serbian competition