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# Go Brilliant

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:

· 11 months, 2 weeks ago

What have you tried? What restrictions can we place on $$m$$? Staff · 11 months, 2 weeks ago

I'm not able to get a start on problems like this.

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