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Part of 2009 Middle European Mathematical Olympiad

Problems(1)

(m + n)^4 = m^2 n^2 + m^2 + n^2 + 6mn

Source: MEMO 2009, problem 7, team competition

(m

n)

of integers which satisfy the equation (m \plus{} n)^4 \equal{} m^2n^2 \plus{} m^2 \plus{} n^2 \plus{} 6mn.

number theory proposednumber theory