Numar natural prim sau compus? |
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batranetupetre |
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Numarul A= (2^2010+1)/2665 este prim sau compus? |
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2665=5*13*41
2^2010+1=(2^10)201 +1=1024^201=(1025-1)^201 +1=(25*41-1)^201+1=M25-1+1=M25
2^2010+1=(2^10)201 +1=1024^201=(1025-1)^201 +1=(25*41-1)^201+1=M41-1+1=M41
2^2010 +1=(2^6)^335+1=64^335 +1=(65-1)^335+1=M13-1+1=M13
Prin urmare numaratorul se divide cu 25, 13 si 41 deci A este numar natural si cum numitorul se divide cu 5 dar nu cu 25, A se divide cu 5, deci este numar compus. |
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