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a+b+c+d=compus

 
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Andrei Ciupan
Euclid


Joined: 27 Sep 2007
Posts: 20

PostPosted: Thu Sep 27, 2007 8:42 pm    Post subject: a+b+c+d=compus Reply with quote

Fie numerele intregi a,b, c, d, astfel incat ab=cd.
Sa se arate ca a+b+c+d nu este numar prim.
[Edit: Modificat de moderator:] Aici nu folosim $, ci [tex] care se inchide cu /tex (tot intre [])
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Andrei Ciupan
Euclid


Joined: 27 Sep 2007
Posts: 20

PostPosted: Fri Sep 28, 2007 8:58 am    Post subject: Reply with quote

Se incearca doua idei:
1.Scrie-l pe  d in functie de  a, b, c si presupune ca  a+b+c+d este prim.

2.Arata ca exista numerele  m, n, p, q astfel incat  a=mn, b=pq, c=np, d=mq.[/tex]
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Claudiu Mindrila
Fermat


Joined: 01 Oct 2007
Posts: 557
Location: Targoviste

PostPosted: Sun Dec 09, 2007 8:19 pm    Post subject: Solutia Reply with quote

Din ab=cd scriem a=xy, b=zt, c=xz, d=yt si atunci avem:
a+b+c+d=xy+yt+xz+zt=(x+t)(y+z) , de unde rezulta cerinta...
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