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Find all pairs \((m,n)\) of non-negative integers for which \[m^2+2\cdot 3^{n}=m \left(2^{n+1}-1\right)\]

Note by Akshat Sharda 11 months, 2 weeks ago

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This is problem N2 (proposed by Austrilia) of the 51st IMO Shortlist (2010).

Official solution:

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What have you tried? What restrictions can we place on \(m\)? – Calvin Lin Staff · 11 months, 2 weeks ago

@Calvin Lin – I'm not able to get a start on problems like this.

Please tell me what approach should I take on problems like these. – Akshat Sharda · 11 months, 2 weeks ago

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TopNewestThis is problem N2 (proposed by Austrilia) of the 51st IMO Shortlist (2010).

– Khang Nguyen Thanh · 11 months, 2 weeks agoOfficial solution:Log in to reply

What have you tried? What restrictions can we place on \(m\)? – Calvin Lin Staff · 11 months, 2 weeks ago

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Please tell me what approach should I take on problems like these. – Akshat Sharda · 11 months, 2 weeks ago

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