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OJM Neamt 2009 subiectul III

 
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Tudor_C
Arhimede


Joined: 08 Mar 2009
Posts: 9

PostPosted: Mon Mar 09, 2009 8:00 pm    Post subject: OJM Neamt 2009 subiectul III Reply with quote

Care este exponentul lui 2 in descompunerea in factori primi a produsului 1964 \cdot 1965 \cdot ........\cdot 2009? In cate zerouri se termina acest produs?
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miruna.lazar
Bernoulli


Joined: 08 Oct 2008
Posts: 224
Location: Tulcea

PostPosted: Tue Mar 24, 2009 10:19 pm    Post subject: Reply with quote

1964\cdot1965\cdot1966\cdot...\cdot2009

1964=2^2\cdot 491
1966=2\cdot 983
1968=2^4\cdot123
1970=2\cdot985
1972=2^2\cdot493
1974=2\cdot987
1976=2^3\cdot247
1978=2\cdot989
1980=2^2\cdot495
1982=2\cdot991
1984=2^6\cdot31
1986=2\cdot993
1988=2^2\cdot497
1990=2\cdot995
1992=2^3\cdot249
1994=2\cdot997
1996=2^2\cdot499
1998=2\cdot999
2000=2^4\cdot125
2002=2\cdot1001
2004=2^2\cdot501
2006=2\cdot1003
2008=2^3\cdot251

Exponentul lui 2 este 45 ( am innebunit ...mi-a luat o ora si jumatate)

1965=5\cdot393
1970=5\cdot394
1975=5^2\cdot79
1980=5\cdot396
1985=5\cdot397
1990=5\cdot398
1995=5\cdot399
2000=5^3\cdot16
2005=5\cdot401

Deci se termina in 12 zerouri.
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DrAGos Calinescu
Thales


Joined: 07 Dec 2008
Posts: 142
Location: Pitesti

PostPosted: Tue Mar 24, 2009 10:32 pm    Post subject: Reply with quote

Nu crezi ca te-ai complicat un pic...
Trebuie sa vezi puterea lui 5 din produs.
Sunt in total
-9 multiplii de 5;
-2 multiplii de 25;
-1 multiplu de 125.
Deci produsul se termina in 12 zero-uri.


Last edited by DrAGos Calinescu on Wed Mar 25, 2009 8:01 pm; edited 1 time in total
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miruna.lazar
Bernoulli


Joined: 08 Oct 2008
Posts: 224
Location: Tulcea

PostPosted: Wed Mar 25, 2009 7:42 pm    Post subject: Reply with quote

Nu erau 12? Embarassed
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DrAGos Calinescu
Thales


Joined: 07 Dec 2008
Posts: 142
Location: Pitesti

PostPosted: Wed Mar 25, 2009 7:59 pm    Post subject: Reply with quote

Am scris eu gresit acum am modificat.
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