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Algebra

Blazing goIITian

Joined:	27 Dec 2010
Post:	1474

11 Feb 2012 23:49:20 IST

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242

comparitively simple.

Mathematics

prove that for any n , we can't further reduce the fraction -

(14n+3)/(21n+4). n should be an integer..

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UTKARSH GARG

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Joined: 1 Mar 2012

Posts: 4

1 Mar 2012 20:32:54 IST

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if (14n+3)/(21n+4) cannot be reduced ,then its reciprocal (21n+4)/(14n+3) cannot be reduced too. now this can be expressed as 1+(7n+1)/(14n+3) . now (7n+1)/(14n+3) has reciprocal (14n+3)/(7n+1) which can be written as 2+1/(7n+1) .now 1/(7n+1) cannot be reduced further as we have 1 in the numerator .hence the initial expression cannot be reduced further whatever be the value of n.

hemang

Blazing goIITian

Joined: 27 Dec 2010

Posts: 1474

3 Mar 2012 01:11:41 IST

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hmmm.

use some modular algebra,

assume some prime divides both the numerator and the denominator.

then , 14n + 3 = 0 (mod p).

21n + 4 = 0(mod p). ....(1)

28n + 6 = 0(mod p). ...(2)

usind (1) and (2), 7n + 2 = 0(mod p).

or, 14n + 4 = 0(mod p).

contradicted.

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