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Algebra

Cool goIITian

Joined:	1 Dec 2007
Post:	31

31 Dec 2007 13:13:32 IST

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328

Factors

None

In how many ways can a integer n be resolved into two factors.

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harsh _27

Blazing goIITian

Joined: 21 Apr 2007

Posts: 897

31 Dec 2007 13:52:10 IST

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the proof comes under number theory ......u just

remember the formula given below

if N is any natural no.

and N = [P1^A1][P2^A2][P3^A3].........[Pk^Ak]

then the no. of ways in which N can be resolved into

product 2 factors is

1/2[A1+1][A2+1][A3+1].......[Ak+1] , if N is

NOT a perfect square

=

1/2{ [A1+1][A2+1][A3+1].......[Ak+1] + 1} , if N is a

perfect square

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