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Un numar compus
Posted: Sun Mar 15, 2009 9:57 am
by mihai miculita
\( \mbox{Demonstrati ca numarul: } 5^{2008}+4 \mbox{ este un numar compus!} \)
(problema C.982 din revista maghiara KOMAL, nr/martie 2009)
Posted: Wed Apr 01, 2009 7:11 pm
by mihai miculita
\( 5^{2008}+4=\left[(5^{1004})^2+2.2.5^{1004}+2^2\right]-4.5^{1004}=(5^{1004}+2)^2-(2.5^{502})^2= (5^{1004}+2-2.5^{502}).(5^{1004}+2+2.5^{502}).
\)
Posted: Wed Apr 01, 2009 8:20 pm
by Radu Titiu
\( a^4+4b^4 \) este intodeauna numar compus.
\( a^4+4b^4=(a^2 +2b^2 +2ab)(a^2+2b^2 -2ab) \)