A line has equation
for some positive integer . The
line passes through the point
for some positive integer . What
is the sum of all possible values of ?
, 2023
Solution
Since the line with equation $y = mx -
50 passes through the point (a,
0)0 = ma - 50$ or
.
Since and are positive integers whose product is
50, then and are a divisor pair of 50.
Therefore, the possible values of
are the positive divisors of 50, which are 1, 2, 5, 10, 25, 50.
The sum of the possible values of
is thus $1 + 2 + 5 + 10 + 25 + 50 =
93$.
Want a route through all this instead of an archive? The track
puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.