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Found problems: 27

2010 Postal Coaching, 2
Tags: real analysis , polynomial , algebra , number theory , quadratic , complex number , sum of roots
Find all non-negative integers $m,n,p,q$ such that \[ p^mq^n = (p+q)^2 +1 . \]

2014-2015 SDML (High School), 6
Tags: algebra , polynomial , sum of roots
Find the largest integer $k$ such that $$k\leq\sqrt{2}+\sqrt[3]{\frac{3}{2}}+\sqrt[4]{\frac{4}{3}}+\sqrt[5]{\frac{5}{4}}+\cdots+\sqrt[2015]{\frac{2015}{2014}}.$$