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October 10th, 2012, 05:15 AM   #1
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Diophantine Fun

This one's pretty challenging but not as hard as we think :

Prove that has no solution in positive integers

Hint : Consider the equation modulo 4



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October 10th, 2012, 06:46 AM   #2
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Re: Diophantine Fun

Pretty easy once you divide out common factors.
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October 10th, 2012, 07:06 AM   #3
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If 3 divides a + b, both a and b must be divisible by 3, so 9 divides a + b, which implies c is divisible by 3.

Hence one could divide all three variables by 3 to get another solution in integers. After sufficient repetition, one must get a = b = c = 0, so this is true to start with, showing that there is no solution in positive integers.
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October 11th, 2012, 09:24 AM   #4
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Re: Diophantine Fun

Originally Posted by mathbalarka

Prove that has no solution in positive integers
Geesh, if Big Pete Pythagoras looked at this quickly, he'd get a heart attack
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