SOLUTION: Hi, I'm stuck with this problem... I don't really know how to tackle it. So if you can help me that'd be much appreciated. Let a be a non-negative integer, written in standard d

Question 792475: Hi, I'm stuck with this problem... I don't really know how to tackle it. So if you can help me that'd be much appreciated.
Let a be a non-negative integer, written in standard decimal notation as
akak−1 . . . a2a1a0, where 0 ≤ ai ≤ 9 for i = 0,1, . . . , k. Prove that a is
divisible by 8 if, and only if, 4a2 + 2a1 +a0 is divisible by 8.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The digits of the number are, in order
, , ...., , and .
Let be the non-negative integer written in standard decimal notation by the first digits.
The value of is

is a non-negative integer

If for some non-negative integer ,
is a multiple of 8.

If is not divisible by 8, then
for some non-negative integers and with , and
is not a multiple of 8.
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