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Kvant 2023
M2740
M2740
Part of
Kvant 2023
Problems
(1)
Easy divisibility
Source: ARO Regional stage 2023 9.4~10.4
2/16/2023
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive integers such that no number divides some other number. If
a
b
−
b
+
1
∣
a
b
c
+
1
ab-b+1 \mid abc+1
ab
−
b
+
1
∣
ab
c
+
1
, prove that
c
≥
b
c \geq b
c
≥
b
.
number theory
Russia