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Portugal MO
2020 Portugal MO
4
sum of 1/ab, for primes a,b
sum of 1/ab, for primes a,b
Source: Portugal OPM 2020 p4
May 15, 2024
number theory
Problem Statement
Determine the fractions of a fraction of the form
1
a
b
\frac{1}{ab}
ab
1
where
a
,
b
a,b
a
,
b
are prime natural numbers such that
0
<
a
<
b
≤
200
0 < a < b \le 200
0
<
a
<
b
≤
200
and
a
+
b
>
200
a + b > 200
a
+
b
>
200
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