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Algebra

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2 May 2008 11:57:47 IST

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Tough one 2^a + 3^b = 5^c abc are integers find abc

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Tough one 2^a + 3^b = 5^c abc are integers find abc

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Celestine Preetham

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2 May 2008 12:01:05 IST

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find all abc satisfying this

tis an olympiad problem
convincing ans to get 3 salutes

Pranav Pant

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2 May 2008 12:06:48 IST

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Two possible solutions are:

a=1, b=1 ,c=1 &

a=4,b=2,c=2

So, abc = 1 or 16.

Celestine Preetham

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2 May 2008 12:13:08 IST

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here u need to find all the a, b ,c and not abc pantprnav

animal

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5 May 2008 12:47:57 IST

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there are only 2 intgral sol a=1,b=1,c=1 and a=4,b=2,c=2.

As we know that if there is 4^a+3^b=5^c then it is a pythagorean triplet and pythagorean triplets have only one integral sol that is 2.

Also graphically if we see then these graphs are like the graph of exponential function which does not have other integral values than the above given values.

hope u got it.

Guess who!!!!!!!

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6 May 2008 10:44:53 IST

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There is one more I can see:

a = 2

b = 0

c = 1

I am trying to get to the solution. I think it is something to do with binomial theorem

animal

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6 May 2008 12:58:00 IST

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i have found all the +ve integral soln. and as oneyeartogo said that a=2,b=0,c=1 is also a soln is correct but i dont think now there r any more soln to this.

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