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We deal with "existence of a solution satisfying the condition of Salem's integral equa- tion", which is an equivalent prediction to Riemann hypothesis. Also We do not consider "boundedness of solution", which is one of the requested conditions, and shown by calcula- tion that the function \(\phi(z)\) defined below is the non-trivial (non-zero) solution of Salem's integral equation.doi:10.5281/zenodo.4312166 fatcat:z7ndltxkdvfltjx6rqbwrc2xuy