Divisible by A?
Consider the following base 4 number:
where each letter represents a different digit between 0 and 3 inclusive.
Assuming A doesn't represent a zero, is the above number divisible by A?
i.e. Is an integer?
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1 solution
"A" must represent 1, 2, or 3.
If it's a 1, then clearly the number divides by 1.
If it's a 2, then the number ends in a 2, which in base 4 is sufficient to conclude that the number divides by 2.
If it's a 3, then you must add up all the digits, and if it divides by 3 then the number divides by 3. This number has two 0's, two 1's, two 2's and two 3's. 0 + 0 + 1 + 1 + 2 + 2 + 3 + 3 = 1 2 which divides by 3.
So, y e s the number is divisible by A .