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2009 Ukraine National Mathematical Olympiad
1
Compare number of prime divisors - [UKRMO 2009 Grade 10]
Compare number of prime divisors - [UKRMO 2009 Grade 10]
Source:
January 23, 2011
Problem Statement
Compare the number of distinct prime divisors of
20
0
2
⋅
20
1
2
⋅
.
.
.
⋅
90
0
2
200^2 \cdot 201^2 \cdot ... \cdot 900^2
20
0
2
⋅
20
1
2
⋅
...
⋅
90
0
2
and
(
20
0
2
−
1
)
(
20
1
2
−
1
)
⋅
.
.
.
⋅
(
90
0
2
−
1
)
.
(200^2 -1)(201^2 -1)\cdot ... \cdot (900^2 -1) .
(
20
0
2
−
1
)
(
20
1
2
−
1
)
⋅
...
⋅
(
90
0
2
−
1
)
.
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