# Let #a,b,c,m# and #n# be integers such that #m<n# and define the quadratic function #f(x) = ax^2+bx+c# where #x# is real. Then #f(x)# has a graph that contains the points #(m,0)# and #(n, 2016^2)#. How many values of #n-m# are possible?

##### 1 Answer

Sep 15, 2016

#### Answer:

#### Explanation:

The graph of

Here,

This means that

Therefore,

No. of possible values of

We have used this result : If the prime factorisation of

then