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\sqrt{ m^2 - 4} < 2\sqrt{n} −m < \sqrt{ m^2 - 2} , diophantine

Source: Indian Postal Coaching 2009 set 4 p6

May 26, 2020

diophantinenumber theoryinequalities

Problem Statement

Find all pairs

(m, n)

of positive integers

m

and

n

for which one has

\sqrt{ m^2 - 4} < 2\sqrt{n} - m < \sqrt{ m^2 - 2}