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The number of values of $$a$$ such that the nine digit number $$8544a5894$$ is divisible by 7 is
The number equals $$854405894 + 10^4 a$$. Here $$854405894 = 7 \times 122057984 + 6$$ and $$10^4 \equiv 4 \pmod 7$$, so we need $$6 + 4a \equiv 0 \pmod 7$$, i.e. $$4a \equiv 1$$ and $$a \equiv 2 \pmod 7$$. Among the digits 0 to 9 this gives $$a = 2$$ or $$a = 9$$, so there are 2 values.
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