4

Part of 2010 Chile National Olympiad

Problems(1)

m + n\sqrt2 = (1 +\sqrt2 )^{2010}

Source: Chile Finals 2010 L2 p4

m, n

integers such that satisfy

m + n\sqrt2 = \left(1 +\sqrt2\right)^{2010} .

Find the remainder that is obtained when dividing

n

5

number theoryalgebra