Excel in math, science, and engineering

New user? Sign up

Existing user? Sign in

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 1 year, 6 months ago

Sort by:

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

Official solution:

Log in to reply

What have you tried? What restrictions can we place on \(m\)? – Calvin Lin Staff · 1 year, 6 months 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 · 1 year, 6 months ago

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

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

– Khang Nguyen Thanh · 1 year, 6 months agoOfficial solution:Log in to reply

What have you tried? What restrictions can we place on \(m\)? – Calvin Lin Staff · 1 year, 6 months ago

Log in to reply

Please tell me what approach should I take on problems like these. – Akshat Sharda · 1 year, 6 months ago

Log in to reply