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ISL 2010 N2

Find all pairs (m,n)(m, n) of nonnegative integers for which m2+2⋅3n=m(2n+1−1)m^{2}+2 \cdot 3^{n}=m\left(2^{n+1}-1\right) (Australia)

Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

Official text: IMO 2010 Shortlist booklet, page 67.

Show the answer

(6,3),(9,3),(9,5),(54,5)

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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