Some Remarks on Number Theory
نویسنده
چکیده
This note contains some disconnected minor remarks on number theory . 1 . Let (1) Iz j I=1, 1 c 1 log k . To prove (2) observe that it immediately follows from the classical theorem of Dirichlet that if I y i I = 1, 1 _5 i 5 n are any n complex numbers, then there is an integer 1 <_ k <_ 10" so that (R(z) denotes the real part of z) 1 (3 ) R(yk) > 2 , 1 S i :5 n . Apply (3) to the n numbers Zrn+l, "',Z(r+1)n, 0 r < oo .'We obtain that there is a k < 10" for which there are infinitely many values of r so that
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