prove that if for some integers a,b,c we have that a^3 +b^3 +c^3 is divisible by 9, then at least one of the number a,b,c is divisible by 3.
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This is not true.
Example a=1 , b=2 , c=3
a3=1 , b3=8 , c3=27
a3+b3+c3=36 which is divisible by 9. However a+b+c=6 which is not.
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