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2021 CHMMC Winter (2021-22)
4
2021-22 Winter Team #4
2021-22 Winter Team #4
Source:
April 17, 2022
number theory
Problem Statement
How many ordered triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of integers
1
≤
a
,
b
,
c
≤
31
1 \le a, b, c \le 31
1
≤
a
,
b
,
c
≤
31
are there such that the remainder of
a
b
+
b
c
+
c
a
ab+bc+ca
ab
+
b
c
+
c
a
divided by
31
31
31
equals
8
8
8
?
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