MathDB

31

Part of 1989 IMO Longlists

Problems(1)

Show that (SQRT(2) + 1)^n = SQRT(m) + SQRT(m-1)

Source: IMO Longlist 1989, Problem 31

9/18/2008
Let n n be a positive integer. Show that \left(\sqrt{2} \plus{} 1 \right)^n \equal{} \sqrt{m} \plus{} \sqrt{m\minus{}1} for some positive integer m. m.
inductionnumber theory unsolvednumber theory