MathDB

2014=a³+2b³/c³+2d³

Source: BMO 2014 - Problem 2

May 4, 2014

3D geometrymodular arithmeticinequalitiesnumber theory unsolvednumber theory

Problem Statement

A special number is a positive integer

n

for which there exists positive integers

a

b

c

, and

d

with

n = \frac {a^3 + 2b^3} {c^3 + 2d^3}.

Prove that
i) there are infinitely many special numbers; ii)

2014

is not a special number.
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