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Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1992 Swedish Mathematical Competition
4
4
Part of
1992 Swedish Mathematical Competition
Problems
(1)
diophantine inequalities a < b, a < 4c, b c^3 <= a c^3 + b
Source: 1992 Swedish Mathematical Competition p4
4/2/2021
Find all positive integers
a
,
b
,
c
a, b, c
a
,
b
,
c
such that
a
<
b
a < b
a
<
b
,
a
<
4
c
a < 4c
a
<
4
c
, and
b
c
3
≤
a
c
3
+
b
b c^3 \le a c^3 + b
b
c
3
≤
a
c
3
+
b
.
inequalities
number theory
diophantine