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2021 BMT
24
BMT 2021 Guts Round p24
BMT 2021 Guts Round p24
Source:
October 7, 2022
algebra
inequalities
number theory
Problem Statement
Suppose that
a
,
b
,
c
a, b, c
a
,
b
,
c
, and p are positive integers such that
p
p
p
is a prime number and
a
2
+
b
2
+
c
2
=
a
b
+
b
c
+
c
a
+
2021
p
a^2 + b^2 + c^2 = ab + bc + ca + 2021p
a
2
+
b
2
+
c
2
=
ab
+
b
c
+
c
a
+
2021
p
. Compute the least possible value of
max
(
a
,
b
,
c
)
\max \,(a, b, c)
max
(
a
,
b
,
c
)
.
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