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Contests
National and Regional Contests
India Contests
India STEMS
2024 India STEMS
STEMS 2024 Math Cat B
STEMS 2024 Math Cat B
Part of
2024 India STEMS
Subcontests
(2)
P5
1
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find all functions satisfying p | f(f(x)) − x^2
Find the sum of all primes
p
<
50
p < 50
p
<
50
, for which there exists a function
f
:
{
0
,
…
,
p
−
1
}
→
{
0
,
…
,
p
−
1
}
f \colon \{0, \ldots , p -1\} \rightarrow \{0, \ldots , p -1\}
f
:
{
0
,
…
,
p
−
1
}
→
{
0
,
…
,
p
−
1
}
such that
p
∣
f
(
f
(
x
)
)
−
x
2
p \mid f(f(x)) - x^2
p
∣
f
(
f
(
x
))
−
x
2
.
P6
1
Hide problems
prove all the rational points are colored the same
All the rationals are coloured with
n
n
n
colours so that, if rationals
a
a
a
and
b
b
b
are colored with different colours then
a
+
b
2
\frac{a+b}2
2
a
+
b
is coloured with a colour different from both
a
a
a
and
b
b
b
. Prove that every rational is coloured with the same colour.