Rezolvarea ecuatiilor diofantice ...tfbias0 tfi-360tli360tjclisttabttx360 SItlistname Stlistid401950534SItlisttlisttemplateid201916417tl istsimpleItlistleveltlevelnfc23tleveljc0tlevelfollo 0tlevelstartat1tlevelspace0tlevelindent0Itleveltext t01tu-3913 SItlevelnumbersStf3tfbias0 tfi-360tli360tjclisttabttx360 SItlistname Stlistid410851262SItlisttlisttemplateid201916421tl istsimpleItlistleveltlevelnfc23tleveljc0tlevelfollo 0tlevelstartat1tlevelspace0tlevelindent0Itleveltext t01tu-3929 SItlevelnumbersStf14tfbias0 tfi-360tli360tjclisttabttx360 SItlistname Stlistid447818851SItlisttlisttemplateid201916421tl istsimpleItlistleveltlevelnfc23tleveljc0tlevelfollo 0tlevelstartat1tlevelspace0tlevelindent0Itleveltext t01tu-3929 SItlevelnumbersStf14tfbias0 tfi-360tli360tjclisttabttx360 SItlistname Stlistid457257315SItlisttlisttemplateid201916431tl istsimpleItlistleveltlevelnfc0tleveljc0tlevelfollo0 tlevelstartat1tlevelspace0tlevelindent0Itleveltextt 02t00.SItlevelnumberst01Stfi-360tli360tjclisttabttx 360 SItlistname Stlistid870268268SItlisttlisttemplateid201916417tl istsimpleItlistleveltlevelnfc23tleveljc0tlevelfollo 0tlevelstartat1tlevelspace0tlevelindent0Itleveltext t01tu-3913 SItlevelnumbersStf3tfbias0 tfi-360tli360tjclisttabttx360 SItlistname Stlistid882131664SItlisttlisttemplateid201916417tl istsimpleItlistleveltlevelnfc23tleveljc0tlevelfollo 0tlevelstartat1tlevelspace0tlevelindent0Itleveltext t01tu-3913 SItlevelnumbersStf3tfbias0 tfi-360tli360tjclisttabttx360 SItlistname Stlistid1778209477SItlisttlisttemplateid201916421t listsimpleItlistleveltlevelnfc23tleveljc0tlevelfoll o0tlevelstartat1tlevelspace0tlevelindent0Itleveltex tt01tu-3929 SItlevelnumbersStf14tfbias0 tfi-360tli360tjclisttabttx360 SItlistname Stlistid1889106486SSIttlistoverridetableItlistover ridetlistid870268268tlistoverridecount0tls1SItlisto verridetlistid410851262tlistoverridecount0tls2SItli stoverridetlistid401950534tlistoverridecount0tls3SI tlistoverridetlistid272053824tlistoverridecount0tls 4SItlistoverridetlistid1778209477tlistoverridecount 0tls5SItlistoverridetlistid369494833tlistoverrideco unt0tls6SItlistoverridetlistid447818851tlistoverrid ecount0tls7SItlistoverridetlistid457257315tlistover ridecount0tls8SItlistoverridetlistid1889106486tlist overridecount0tls9SItlistoverridetlistid882131664tl istoverridecount0tls10SSItinfoIttitle Rezolvarea ecuatfeiilor diofanticeSItauthor Raluca Musaloiu-ElefteriSItoperator Raluca Musaloiu-ElefteriSItcreatimtyr1999tmo7tdy8thr17tmi n25SItrevtimtyr1999tmo7tdy8thr17tmin25SItprintimtyr 1999tmo1tdy13thr1tmin7SItversion2SItedmins0SItnofpa ges5SItnofords847SItnofchars4832SItnofcharss5934SIt vern71SStpaper11906tpaperh16838tmargt1135 tidoctrltftnbjtaenddoctformshadetviekind1tviescale 100tpgbrdrheadtpgbrdrfoot tfet0tsectd tlinex0theadery709tfootery709tcolsx709tendnheretse ctdefaultcl Itfooter tpardtplain ts16tqctnoidctlpartidctlpartbrdrttbrdrstbrdr10tbrs p20 ttqcttx4153ttqrttx8306tadjustright tfs20tlang1048tcgrid I- SItfieldIttfldinst Itcs17 PAGE SSItfldrslt Itcs17tlang1024 1SSSItcs17 SItfieldIttfldinst Itcs17 NUMPAGES SSItfldrslt Itcs17tlang1024 1SSSItcs17 -SItpar SSIttpnseclvl1tpnucrmtpnstart1tpnindent720tpnhangI tpntxta .SSIttpnseclvl2tpnucltrtpnstart1tpnindent720tpnhan gItpntxta .SSIttpnseclvl3tpndectpnstart1tpnindent720tpnhangI tpntxta .SSIttpnseclvl4tpnlcltrtpnstart1tpnindent720tpnhan gItpntxta SSIttpnseclvl5tpndectpnstart1tpnindent720tpnhangIt pntxtb SItpntxta SSIttpnseclvl6tpnlcltrtpnstart1tpnindent720tpnhang Itpntxtb SItpntxta SSIttpnseclvl7tpnlcrmtpnstart1tpnindent720tpnhangI tpntxtb SItpntxta SSIttpnseclvl8tpnlcltrtpnstart1tpnindent720tpnhang Itpntxtb SItpntxta SSIttpnseclvl9tpnlcrmtpnstart1tpnindent720tpnhangI tpntxtb SItpntxta SStpardtplain ts1tqjtsb240tsa60tkeepntnoidctlpartidctlpartoutlin elevel0tadjustright tbtf1tfs28tlang1048tkerning28tcgrid Itf70 Rezolvarea ecuatfeiilor diofanticetpar Stpardtplain ts15tqjtnoidctlpartidctlpartadjustright tfs20tlang1048tcgrid Itpar SItf70 Orice congruentfete3 SIti axSItitsub 1SIti cSIti ItfieldIttfldinst SYMBOL 186 ttf Symbol tts 10SItfldrslttf3tfs20SSSIti 0 mod bSItf70 se poate scrie ca o ecuatfeie SIti axSItitsub 1SIti bxSItitsub 2SIti c0SI teen care SIti aSIti ItfieldIttfldinst SYMBOL 185 ttf Symbol tts 10SItfldrslttf3tfs20SSSIti 0SI, SIti bSIti ItfieldIttfldinst SYMBOL 179 ttf Symbol tts 10SItfldrslttf3tfs20SSSItitf70 1 tbai c, xSItitsub 1SIti , xSItitsub 2SItf70 sunt numere teentregi. Dacte3 SIti a, b, cSItf70 sunt numere teentregi date tbai SIti xSItitsub 1SItitf70 tbai xSItitsub 2SI sunt considerate necunoscute, problema se redSItf70 uce la gte3sirea solutfeiilor teentregi ale unei ecuatfeii liniare cu coeficientfei teentregi. Daca SIti fxSItitsub 1SIti ,t85, xSItitsub nSIti SI este un polinom teen SIti xSItitsub 1SIti ,t85, xSItitsub nSItf70 cu coeficientfei teentregi, atunci ecuatfeia SIti fxSItitsub 1SIti ,t85, xSItitsub nSIti ASItf70 se numetbate SItbtf70 diofanticte3 SItf70 dacte3 solutfeiile ei sunt numere teentregi. Denumirea acestor ecuatfeii derivte3 de la numele matematicianului grec SItb DiofantosSItf70 din Alexandria. Dacte3 o astfel de ecuatfeie admite solutfeii, atunci ea admite o infinitate de SIti nSI-upluri care o satisfac.tpar tpar tcen continuare se va trata cazul n2 SItfs24 axbyctpar SItpar SItf70 Dacte3 SIti aSItf70 tbai SIti bSI sunt numere prSItf70 ime teentre ele tbai SIti xSItitsub 0SI, SIti ySItitsub 0SItf70 constituie o solutfeie pentru SIti axbycSItf70 , atunci totalitatea solutfeiilor se poate reprezenta sub forma SIti x xSItitsub 0SIti btSI, SIti y ySItitsub 0SIti tendash atSI, unde SIti tSItf70 este un numte3r teentreg oarecare. O solutfeie a ecuatfeiei se poate obtfeine cu ajutorul penultimei fractfeii de aproximare pentru reprezentarea sub formte3 de fractfeie continute3 a lui SIti abSItf70 . Considerte2nd cte3 penultima fractfeie este SIti mnSI, SIti xSItitsub 0SIti nc, ySItitsub 0SIti -mc.tpar SItpar SItbti Exemplutpar tpar SItf70 Fie ecuatfeia 43x19y2.tpar SItpar SItf70 Fractfeiile de aproximare ale lui 4319 sunt 73, 94, 4319.tpar SItpar SItlang1024 ItshpIttshpinsttshpleft792tshptop63tshpright6732ts hpbottom1282tshpfhdr0tshpbxcolumntshpbyparatshpr1ts hprk0tshpfbltxt0tshpz0tshplid1027ItspItsn shapeTypeSItsv 75SSItspItsn fFlipHSItsv 0SSItspItsn fFlipVSItsv 0SSItspItsn pibSItsv Itpicttpicscalex100tpicscaley100tpiccropl0tpiccrop r0tpiccropt0tpiccropb0tpic10478tpich2150tpicgoal594 0tpichgoal1219tmetafile8tbliptag504379189tblipupi41 4Ittblipuid 1e103735c7063503fa0b65fad26c48cdS01000900000393020 000040015000000000005000000090200000000040000000201 0100050000000102ffffff00040000002e01180005000000310 201000000050000000b0200000000050000000c02a007202512 00000026060f001a00ffffffff000010000000c0ffffffb6fff fffe0240000560700000b00000026060f000c004d6174685479 70650000a00209000000fa02000010000000000000002200040 000002d010000050000001402000240000500000013020002dc 010500000014020002c2050500000013020002400709000000f a02000008000000000000002200040000002d01010005000000 1402e803460b050000001302e803c40c040000002d010000050 0000014020002260b0500000013020002e40c040000002d0101 00050000001402e8030... 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