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n^2=a+b, n^3=a^2+b^2

Source: Dutch BxMO/EGMO Team Selection Test 2014 P1

July 17, 2014

number theory proposednumber theory

Problem Statement

Find all non-negative integer numbers

n

for which there exists integers

a

and

b

such that

n^2=a+b

and

n^3=a^2+b^2.