Question

what is the least positive integer n such that 2n-1/n+7 is an integer.​

Answer 1

Answer:

Consider the lines y=2x−1 and y=x+7.

From (−∞,8) , y=2x−1 is greater than y=x+7. Obviously, in such a condition, the quotient cannot be an integer. So, the point at which the quotient gives integer values must be such that x>=n where n is the abcissa of the intersections point of the two lines.

At, (8,15), the two lines intersect. Thus these lines intersect at a lattice point.