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Determinati cel mai mare numar natural n, astfel incat 2^n | ( 2 x 4 x 6 x ... x 50 )

Răspuns :

[tex]2*4*6*8*....*50= \\ (2*1)*(2*2)*(2*3)*(2*4)*.....*(2*25) \\ 2^{25}*1*2*3*4*5*6*...*25.[/tex]
Puterea la care se gaseste 2 in produsul [tex]1*2*3*4*5*6*7*......*25[/tex] se afla dupa formula: [tex][\frac{25}{2}]+[\frac{25}{2^{2}}]+[\frac{25}{2^{3}}]+[\frac{25}{2^{4}}]+[\frac{25}{2^{5}}]=12+6+3+1+0=22[/tex]
[] reprezinta partea intreaga
Deci n=25+22=47