@Kitonum 

Verify that y 􏰐 = -􏰀 (a/2)*x 􏰏+ (a^2)/8 􏰀- (1/2) is a solution for all cases when a 􏰘 =< 0. 

Show that this is the only straight line solution in these cases. 

on maple ive started it 

y := -(1/2)*a*x+(1/8)*a^2-1/2;
sqrt(a*x+2*y+1);

and got

(1/2)* sqrt(a^2)

as answer how would i do the rest on maple

@tomleslie sorry i made corrections to my question

@Kitonum i have four plots that need to be ouputted by your mentioned command I have got them 4 in a row but I would like them 2 by 2 but in one figure how is this possible?

@Kitonum from your previous answer for part iv i did

A:=-(cos((t/n)+t))/(sin((t/n)+t)):

sol:=solve(denom(A)=0,t,allsolutions):

indets(%)[1]:
h:=subs(%=1, sol):
n*Pi/h
                             n + 1

how could i do part v on its own without linking back?

thank you!

@Kitonum thank you for that answer it was so easy to follow through. the next part is 

(v) By referring to appropriate sketches, show that the result in part (iv) is true in the case n = 4. 

in solution it says

@acer I

@dharr that worked

This is what happens in Maple

@Kitonum when i copy the text into the worksheet the power is displayed as ^2 and the factorial does not show so i correct them and all numbers from 2-1000 are printed.

Hi when i type taht exactly how you have written in maple it says there is an error  'Error, invalid terms in sum: 1 .. 1000'. how can i solve this. thank you for your help.

@tomleslie thank you so much i got the answers. Would it be possible to make this into a small program maybe using a for loop or would that not be possible. 

In python 3 it shows a program like this

def prog1(p):

for i in range (0,p):

if (i*i)%p==p-1:

print(i)

i am new to maple sorry about this

@tomleslie hi thank you for your answer. How would i do it if the p value was fixed not a range of p values. So i can keep running the program by just changing the p value to something different not a range