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ãáÎÕ ÚÇã Ýí ÇáÑíÇÖíÇÊ
ááÓäÉÇáÑÇÈÚÉ ãÊæÓØ
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¨ ÇáÚÏÏÇä ÇáÃæáíÇä ÝíãÇ ÈíäåãÇ åãÇ ÇáÚÏÏÇä ÞÇÓãåãÇ ÇáãÔÊÑß ÇáÃßÈÑ íÓÇæí 1 Ãí 1 = PGCD .
¨ ÇáßÓÑ ÇáÛíÑ ÞÇÈá ááÇÎÊÒÇá åæ ÇáßÓÑ ÈÓØå æãÞÇãå ÃæáíÇä ÝíãÇ ÈíäåãÇ .
¨ áÅíÌÇÏ ÇáÞÇÓã ÇáãÔÊÑß ÇáÃßÈÑ äÊÈÚ ÃÍÏ ÇáØÑÞ ÇáÊÇáíÉ:
1. äÈÍË Úä ÌãíÚ ÇáÞæÇÓã ÇáãÔÊÑßÉ æäÃÎÐ ÃßÈÑåÇ .
2. ÚãáíÉ ÇáØÑÍ ÇáãÊÊÇáíÉ .
3. ÇáÞÓãÉ ÇáÅÞáíÏíÉ .





¨ áÌÚá ãÞÇã ÇáäÓÈÉ [You must be registered and logged in to see this image.] ÚÏÏÇ äÇØÞÇ äÖÑÈ ßáÇ ãä ÇáÈÓØ ÇáãÞÇã Ýí ÇáãÑÇÝÞ Ãí :äÖÑÈ[You must be registered and logged in to see this image.] æ[You must be registered and logged in to see this image.] Þí ÇáÚÏÏ [You must be registered and logged in to see this image.]
¨ [You must be registered and logged in to see this image.]ãÚÇÏáÉ ãä ÇáÏÑÌÉ ÇáÃæáì ÐÇÊ ãÌåæá æÇÍÏ .
¨ Íá ÇáãÚÇÏáÉ ãä ÇáÏÑÌÉ ÇáÃæáì ÐÇÊ ãÌåæá æÇÍÏ åæ ÅíÌÇÏ ãÌãæÚÉ ÍáæáåÇ Ãí ÇáÃÚÏÇÏ ÇáÊí ÊÍÞÞ ÇáãÓÇæÇÉ.
¨ áÍá ÇáãÓÃáÉ íÌÈ :
1. ÞÑÇÁÉ äÕ ÇáãÓÃáÉ æÝåãåÇ æÊÍÏíÏ ÇáãÚØíÇÊ .
2. ÇÎÊíÇÑ ÇáãÌåæá .
3. ÊÑÌãÉ ÇáãÚØíÇÊ æßÊÇÈÊåÇ Ýí ÕíÛÉ ÇáãÚÇÏáÉ .
4. ÇáÞíÇã ÈÍá ÇáãÚÇÏáÉ .


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¨ ßá ÚÈÇÑÉ ãä ÇáÔßá :[You must be registered and logged in to see this image.] ¡ [You must be registered and logged in to see this image.] ¡ [You must be registered and logged in to see this image.] ¡ [You must be registered and logged in to see this image.] ÊÓãì ãÊÑÇÌÍÇÊ ãä ÇáÏÑÌÉ ÇáÃæáì ÈãÌåæá æÇÍÏ.
¨ Íá ÇáãÑÇÈÍÉ ãä ÇáÏÑÌÉ ÇáÃæáì ÈãÌåæá æÇÍÏ åæ ÅíÌÇÏ ßá ÇáÞíã ÇáããßäÉ ááãÌåæá ÍÊì Êßæä ÇáãÊÈÇíäÉ
ÇáÕÍíÍÉ


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¨ ßá ÏÇáÉ ÊßÊÈ Úáì Ôßá :[You must be registered and logged in to see this image.] ÊÓãì ÏÇáÉ ÎØíÉ æÊãËíáåÇ ÇáÈíÇäí ÚÈÇÑÉ Úä ÎØ ãÓÊÞíã íãÑ ÈÇáãÈÏÃ.
¨ ßá ÏÇáÉ ÊßÊÈ Úáì Ôßá :[You must be registered and logged in to see this image.] ÊÓãì ÏÇáÉ ÊÂáÝíÉ æÊãËíáåÇ ÇáÈíÇäí ÚÈÇÑÉ Úä ÎØ ãÓÊÞíã áÇ íãÑ ÈÇáãÈÏÃ.
¨ ÇáäÓÈ ÇáãÆæíÉ :
v ÍÓÇÈ [You must be registered and logged in to see this image.] ãÚäÇå : [You must be registered and logged in to see this image.].
v ÒíÇÏÉ [You must be registered and logged in to see this image.] ÈÜ [You must be registered and logged in to see this image.] ãÚäÇå : [You must be registered and logged in to see this image.].
v ÇäÎÝÇÖ [You must be registered and logged in to see this image.] ÈÜ [You must be registered and logged in to see this image.] ãÚäÇå : [You must be registered and logged in to see this image.].
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¨ ÌãáÉ ãÚÇÏáÊíä ãä ÇáÏÑÌÉ ÇáÃæáì ÈãÌåæáíä [You must be registered and logged in to see this image.] æ [You must be registered and logged in to see this image.] åí ÌãáÉ ãä ÇáÔßá:[You must be registered and logged in to see this image.]
¨ Íá ÌãáÉ ãÚÇÏáÊíä ãä ÇáÏÑÌÉ ÇáÃæáì ÈãÌåæáíä [You must be registered and logged in to see this image.]æ [You must be registered and logged in to see this image.]åæ ÅíÌÇÏ ÇáËäÇÆíÉ [You must be registered and logged in to see this image.] ÇáÊí ÊÍÞÞ ÇáãÚÇÏáÊíä Ýí Âä æÇÍÏ.
¨ áÍá ÇáÌãáÉ ÌÈÑíÇ äÊÈÚ ÃÍÏ ÇáØÑÞ:
v ØÑíÞÉ ÇáÊÚæíÖ.
v ØÑíÞÉ ÇáÌãÚ.
v ØÑíÞÉ ÇáÌãÚ æ ÇáÊÚæíÖ.

¨ íãßä Íá ÇáÌãáÉ ÈíÇäíÇ æÐáß ÈÅíÌÇÏ äÞØÉ ÊÞÇØÚ ÇáãÓÊÞíãíä (ÅÍÏÇËíÇÊåÇ ).



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¨ ÌíÈ ÊãÇã æÌíÈ æÙá ÒÇæíÉ ÍÇÏÉ :
v [You must be registered and logged in to see this image.]. Ãí ÇáãÞÇÈá Úáì ÇáãÌÇæÑ.
v [You must be registered and logged in to see this image.]. Ãí ÇáãÞÇÈá Úáì ÇáæÊÑ.
v [You must be registered and logged in to see this image.].Ãí ÇáãÌÇæÑ Úáì ÇáæÊÑ.

¨ ÎæÇÕ :
v [You must be registered and logged in to see this image.].
v [You must be registered and logged in to see this image.].
v ãËáË ÞÇÆã Ýí [You must be registered and logged in to see this image.] ÝÅä. (ÎÇÕíÉ ÝíËÇÛæÑÓ).



[You must be registered and logged in to see this image.] ãÓÊÞíãÇä ãÊÞÇØÚÇä Ýí ÇáäÞØÉ A





¨ ÅÐÇ ßÇä ( BC) // ( MN) ÝÅä : [You must be registered and logged in to see this image.] = [You must be registered and logged in to see this image.] = [You must be registered and logged in to see this image.]
¨ ÅÐÇ ßÇä [You must be registered and logged in to see this image.] = [You must be registered and logged in to see this image.] ÝÅä ( BC ) // ( MN) .




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ÇáãÍíØ ([You must be registered and logged in to see this image.])
ÇáãÓÇÍÉ ([You must be registered and logged in to see this image.])
ãáÇÍÙÉ
ÇáãÑÈÚ
[You must be registered and logged in to see this image.] Øæá ÖáÚ ÇáãÑÈÚ
ÇáãÓÊØíá
[You must be registered and logged in to see this image.] Øæá æ[You must be registered and logged in to see this image.] ÚÑÖ ÇáãÓÊØíá
ÇáãËáË
[You must be registered and logged in to see this image.] ÞÇÚÏÉ æ[You must be registered and logged in to see this image.]ÇÑÊÝÇÚ ÇáãËáË
ÔÈå ÇáãäÍÑÝ
[You must be registered and logged in to see this image.]ÇáÞÇÚÏÉ ÇáßÈÑì
[You must be registered and logged in to see this image.] ÇáÞÇÚÏÉ ÇáÕÛÑì
ÇáÞÑÕ
[You must be registered and logged in to see this image.] äÕÝ ÇáÞØÑ
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ÇáÍÌã ([You must be registered and logged in to see this image.])
ÇáãÓÇÍÉ ([You must be registered and logged in to see this image.])
ãáÇÍÙÉ
ÇáãßÚÈ
[You must be registered and logged in to see this image.] Øæá ÖáÚ ÇáãßÚÈ
ãÊæÇÒí ÇáãÓÊØíáÇÊ
[You must be registered and logged in to see this image.] ãÍíØ ÇáÞÇÚÏÉ
ÇáãæÔæÑ ÇáÞÇÆã
[You must be registered and logged in to see this image.] ãÓÇÍÉ ÇáÞÇÚÏÉ
ÇáßÑÉ
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ÇáÞÑÕ
[You must be registered and logged in to see this image.] äÕÝ ÇáÞØÑ
ÇáåÑã
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ÇáãÎÑæØ
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¨ Ýí ãÚáã¡ äÚÊÈÑ ÇáäÞØÊíä [You must be registered and logged in to see this image.] æ [You must be registered and logged in to see this image.]
v ÅÍÏÇËíÇÊ ÔÚÇÚ:[You must be registered and logged in to see this image.].
v ÅÍÏÇËíÇÊ ãäÊÕÝ ÞØÚÉ : [You must be registered and logged in to see this image.]ãäÊÕÝ ÇáÞØÚÉ [You must be registered and logged in to see this image.] íÚäí :[You must be registered and logged in to see this image.].
v Øæá ÞØÚÉ ãÓÊÞíã :[You must be registered and logged in to see this image.]
¨ ÇáÊßÑÇÑ ÇáãÌãÚ ÇáãÊÒÇíÏ : Ýí ÓáÓáÉ ÅÍÕÇÆíÉ ãÑÊÈÉ ÊÑÊíÈÇ ÊÕÇÚÏíÇ¡ ÇáÊßÑÇÑ ÇáãÌãÚ ÇáãÊÒÇíÏ áÞíãÉ íÍÕá
Úáíå ÈÌãÚ ÊßÑÇÑ åÐå ÇáÞíãÉ æÊßÑÇÑ ÇáÞíã ÇáÓÇÈÞÉ áåÇ.
¨ ÇáÊßÑÇÑ ÇáãÌãÚ ÇáãÊäÇÞÕ: Ýí ÓáÓáÉ ÅÍÕÇÆíÉ ãÑÊÈÉ ÊÑÊíÈÇ ÊÕÇÚÏíÇ¡ ÇáÊßÑÇÑ ÇáãÌãÚ ÇáãÊäÇÞÕ áÞíãÉ íÍÕá Úáíå ÈÌãÚ ÊßÑÇÑ åÐå ÇáÞíãÉ æÊßÑÇÑ ÇáÞíã ÇáÃßÈÑ ãäåÇ.


¨ ÇáÊßÑÇÑ ÇáäÓÈí ÇáãÌãÚ ÇáãÊÒÇíÏ æÇáãÊäÇÞÕ:
v ÇáÊßÑÇÑ ÇáäÓÈí ÇáãÌãÚ ÇáãÊÒÇíÏ = ÇáÊßÑÇÑ ÇáãÌãÚ ÇáãÊÒÇíÏ Úáì ÇáÊßÑÇÑ Çáßáí .
v ÇáÊßÑÇÑ ÇáäÓÈí ÇáãÌãÚ ÇáãÊäÇÞÕ = ÇáÊßÑÇÑ ÇáãÌãÚ ÇáãÊäÇÞÕ Úáì ÇáÊßÑÇÑ Çáßáí .
¨ ÇáæÓØ ÇáÍÓÇÈí áÓáÓáÉ : [You must be registered and logged in to see this image.]
v ÇáæÓØ ÇáÍÓÇÈí áÓáÓáÉ ÅÍÕÇÆíÉ åæ ãÌãæÚ Þíã åÐå ÇáÓáÓáÉ Úáì ÚÏÏ ÞíãåÇ.
v ÇáæÓØ ÇáÍÓÇÈí ÇáãÊæÇÒä áÓáÓáÉ ÅÍÕÇÆíÉ åæ ãÌãæÚ ÌÏÇÁÇÊ ÞíãåÇ ÈÊßÑÇÑÇÊåÇ Úáì ãÌãæÚ
ãÚÇãáÇÊ ÇáÊßÑÇÑÇÊ.
¨ ÇáæÓíØ :
v ÅÐÇ ßÇä ÚÏÏ Þíã ÇáÓáÓáÉ ÝÑÏí¡ ÇáæÓíØ åæ ÇáÞíãÉ ÇáÊí ÊÊæÓØ ÇáÓáÓáÉ ÈÚÏ ÊÑÊíÈåÇ.
v ÅÐÇ ßÇä ÚÏÏ Þíã ÇáÓáÓáÉ ÒæÌí¡ ÇáæÓíØ åæ ÇáãÊæÓØ ÇáÍÓÇÈí ááÞíãÊíä ÇááÊÇä ÊÞÚÇä Ýí ÇáÑÊÈÊÇä :
[You must be registered and logged in to see this image.] æ [You must be registered and logged in to see this image.] ÍíË [You must be registered and logged in to see this image.]ÚÏÏ Þíã ÇáÓáÓáÉ.
v ÅÐÇ ßÇäÊ ÇáÓáÓáÉ ãÌãÚÉ Ýí ÝÆÇÊ äÈÍË Úä ÇáÝÆÉ ÇáÊí ÊäÊãí ÅáíåÇ ÇáÞíãÉ ÇáæÓØíÉ.
¨ ÇáãÏì: ãÏì ÓáÓáÉ ÅÍÕÇÆíÉ åæ ÇáÝÑÞ Èíä ÃßÈÑ ÞíãÉ æ ÃÕÛÑ ÞíãÉ áåÇ .
¨

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