jmc

Question

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:

If 2 x \equiv y + 5 (mod 9), then x \equiv y + (mod 9) .

What is the product of the two digits that go in the blanks?

Accepted Answer

Multiplying both sides of the congruence 2x y+5 9by 5 gives 10x 5y+25 9,then reducing both sides modulo 9 gives x 5y+7 9.Thus, the product of the blanks is 5 7=35.