Exactly one of the following numbers cannot be written as a3 + b3 where a and b are integers.
Which number is it?
Choices:
A) 700056	B) 707713	C) 7000639	D) 7077283	E) 7077915
If a is an integer, then a3 gives remainder 0, 1, or 6 when divided by 7 (just consider the   remainders of 03, 13, 23, 33, 43, 53, and 63 when divided by 7). Then a3 + b3 gives remainder   0, 1, 2, 5, or 6 when divided by 7. Well, 7077283 gives remainder 3 when divided by 7. (The   remaining numbers can be represented as a sum of two cubes of integers, 700056 = 403 + 863,   707713 = 143 + 893, 7000639 = 323 + 1913, and 7077915 = 33 + 1923.)   correct answer 7077283
<result>D</result>
Exactly one of the following numbers cannot be written as a3 + b3 where a and b are integers.
Which number is it?