PROBLEMAI GOLDBAKh

PROBLEMAI GOLDBAKh, yake az problemahoi mashhuri nazariyai adadhoet, ki sharhash chunin ast: har guna adadi butuni az shash kalon yo ba on barobarro dar shakli hosili jami se adadi sodda ifoda kardan mumkin ast. Soli 1742 X. Gold­bakh ba L. Eyler maktub navishta in problemaro pesh guzoshta bud. L. Eyler dar javob qayd namud, ki ba­roi halli muammoi mazkur isbot kardani iborai «har yak adadi juft az summai du adadi sodda iborat ast» kofist. Dar tuli qarnho ba hej yak matematik muyassar nagardid, ki in problemaro hal namoyad. Soli 1923 G. Khardi va J. Litlvud is­bot kardand, ki agar baze teoremahoi mutaalliqi qatorhoi Di­rikhle durust boshand, on goh har guna adadi nisbatan kaloni toq az summai se adadi sodda iborat ast. Soli 1930 matematiki soveti L. G. Shnirelman teoremaero is­bot namud, ki mazmunash in ast: «adadi dilkhohi butuni az yak kalon ba summai miqdori malumi adadhoi sodda barobar ast». In teorema baroi halli P. G. takon dod. Soli 1937 I. M. Vinogradov isbot kard, ki har guna adadi nisbatan kaloni toqro ba namudi summai se adadi sodda ifoda kardan mumkin ast. Hamin tavr halli L. G. baroi adadhoi toq yofta shud. Halli mazkur az komyobihoi buzurgi matematikai muosir donista shud. Sonitar halli digarn in teoremaro matematiki soveti Yu. V. Linnik (1945) peshnihod kard. Masalai az summai du adadi sodda iborat budani ada­di juft to hol (1984) hal nashudaast.

Ad.: Vinogradov I. M., Metod trigonometricheskikh summ v teorii chi­sel, M., 1971; Karasuba A. A., Os­novi analiticheskoy teorii chisel, M.,