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?

MIRB16
Jun 9, 2018