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diophantine inequalities a < b, a < 4c, b c^3 <= a c^3 + b

Source: 1992 Swedish Mathematical Competition p4

April 2, 2021
inequalitiesnumber theorydiophantine

Problem Statement

Find all positive integers a,b,ca, b, c such that a<ba < b, a<4ca < 4c, and bc3≤ac3+bb c^3 \le a c^3 + b.
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