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Contests
National and Regional Contests
Netherlands Contests
Dutch IMO TST
2023 Dutch IMO TST
2023 Dutch IMO TST
Part of
Dutch IMO TST
Subcontests
(2)
1
1
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3^p+4^p+5^p+9^p-98 has at most 6 positive divisors
Find all prime numbers
p
p
p
such that the number
3
p
+
4
p
+
5
p
+
9
p
−
98
3^p+4^p+5^p+9^p-98
3
p
+
4
p
+
5
p
+
9
p
−
98
has at most
6
6
6
positive divisors.
4
1
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Ridiculous FE with straight bash
Find all functions
f
:
Q
+
→
Q
f: \mathbb{Q^+} \rightarrow \mathbb{Q}
f
:
Q
+
→
Q
satisfying
f
(
x
)
+
f
(
y
)
=
(
f
(
x
+
y
)
+
1
x
+
y
)
(
1
−
x
y
+
f
(
x
y
)
)
f(x)+f(y)= \left(f(x+y)+\frac{1}{x+y} \right) (1-xy+f(xy))
f
(
x
)
+
f
(
y
)
=
(
f
(
x
+
y
)
+
x
+
y
1
)
(
1
−
x
y
+
f
(
x
y
))
for all
x
,
y
∈
Q
+
x, y \in \mathbb{Q^+}
x
,
y
∈
Q
+
.