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B,C from A (Posted on 2007-09-14) Difficulty: 3 of 5
A(=abcde) is a 5-digit natural number with no leading zeros and e>a. B(=eca), 3-digit natural number is a multiple of 9 while C(=db), 2-digit natural number is a multiple of 3 but not 9.
Show that x5-y5=A has no integer solutions if sum of digits of C is not 6.

Note: A(=abcde) means Ten Thousand's digit of A:a, Thousand's digit of A:b and so on unit's digit of A:e.

See The Solution Submitted by Praneeth    
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Hints/Tips Hint | Comment 1 of 6
For the equation take modulo 11 on both sides.
Now evaluate A mod 11.

  Posted by Praneeth on 2007-09-17 00:32:58
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