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# help with 2 (one unaswered)

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In the statement below, the two blanks can be filled by positive single-digit numbers in such a way that the statement is always true: $$\text{If }2x\equiv y+5\ (\bmod\ 9)\text{, then }x\equiv \underline{\ \ \ }\,y+\underline{\ \ \ }\ (\bmod\ 9).$$What is the product of the two digits that go in the blanks?

Suppose m is a two-digit positive integer such that $$6^{-1}\pmod m$$ exists and $$6^{-1}\equiv 6^2\pmod m.$$ What is m?

Jun 9, 2018