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Dangerous Expression for Rationals (Posted on 2013-03-31) Difficulty: 3 of 5
Prove or disprove the following statement:

Each positive rational number can be written in the form: (a^2+b^3)/(c^5+d^7)
where a,b,c,d are positive integers.

No Solution Yet Submitted by Danish Ahmed Khan    
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re(2): Question? | Comment 4 of 5 |
(In reply to re: Question? by Charlie)

Sorry I worded it wrongly.

The possibilities of numerator expression are 2,5,9,10,12,17,24,26,28,31,33,36,37,43,44,52....... and of denominator expression are  2,33,129,160,244,371,1025, 1152,2188,3126,3211,3253....... which leaves very few possibilities of generating all possible numbers from these sets. Especially ratios of primes or ratios of higher powers of primes different from the powers used in expression. ( like 4,6 etc ) 

Then again similar multiple of primes can be a possibility.

 

 


  Posted by Salil on 2013-04-05 07:10:48
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