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Modular Fractions

Age 16 to 18 Challenge Level:

$$3^{-1}+6^{-1} = 5 + 6 = 11 = 4 \pmod 7$$

and

$$(3+6)^{-1} = 9^{-1} = 2^{-1} = 4 \pmod 7$$

so $x=3,\ y=6$ is one solution. Now find the other solutions.