49 = 9*4 + 9 + 4
I don't believe that 48 can be written
Let's suppose that it can.....we have
a( b+ 1) + b = 48
ab + a + b = 48
ab + b = 48 - a
b ( a + 1) = 48 - a
b = 48 - a
______
a + 1
"a" cannot be odd because we would have odd / even = no integer possible for "b"
Possible values for a, b
a b
0 48 not possible.....a,b must be positive
6 6 not unique for a, b
And no "a" from 8 - 22 inclusive will produce an integer
And if a > 22 and even....then we will have a proper fraction for "b".... [ not an integer ]
So.....48 is the largest integer that cannot be written