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Prove that the fractional part of x exceeds 10^{-19.76}.

Source:

January 28, 2011

floor functionnumber theory unsolvednumber theory

Problem Statement

Let

x =\sqrt{a}+\sqrt{b}

, where

a

and

b

are natural numbers,

x

is not an integer, and

x < 1976

. Prove that the fractional part of

x

exceeds

10^{-19.76}