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 x

^{5}-y

^{5}=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.

(In reply to

Solution (using Excel) by hoodat)

a. your C is wrong- not as defined

b. the final answers do not comply with the specs i.e d+b =6 ??you show that there are no numbers to fullfil the original requirements