#OK to post homework
#Tianyi Liu, Dec13, Assignment 25

1.
1, 1, 1, 1, 1, 1, 1, 1, 1
1, 1, 1, 1, 1, 1
1, 1, 1, 1, 1
1, 1, 1
1
1
1
[7,4,4,3,3,2,1,1,1]

2.
79811865

3.
[[6,5,3,1,1,1,1,1],-1]
8+3(-1)=5<6
[6,4,2,2,2,2,2],0

BZ([[6,5,3,1,1,1,1,1],-1])
[[6, 4, 2, 2, 2, 2, 2], 0]

4.
I did not get the error message with pnFast(10000).
pnFast(10000) and [seq(PnFast(i),i=1..10000)][10000] take the same amount of time to compute.
pnFast(20000);
252114813812529697916619533230470452281328949601811593436850314108034284423801564956623970731689824369192324789351994903016411826230578166735959242113097

5.
pnFastMod:=proc(n,m) local s:
s:=[seq(PnFast(i),i=1..n)][n]:
s mod m:
end:

27493510569775696512677516320986352688173429315980054758203125984302147328114964173055050741660736621590157844774296248940493063070200461792764493033510116079342457190155718943509725312466108452006369558934464248716828789832182345009262853831404597021307130674510624419227311238999702284408609370935531629697851569569892196108480158600569421098519

6.
InvGlashier:=proc(M) local s,L,i,S:
L:=[]:
S:=[op(M),0]:
s:=1:
for i from 1 to nops(S)-1 do 
 if S[i]=S[i+1] then
  s:=s+1:
 else
  L:=[op(L),s]:
  s:=1:
 fi:
od:
for j from 1 to nops(L) do
 a:=L[j]:
 count:=0:
 while a>1 do
  a:=a mod 2:
  count:=count+1:
 od:
L1:=[op(L1),]

end:

finder:=proc(n) local st,count,a,L:
st:=n:
count:=0:
L:=[]:

while st>1 do
 a:=st:

 while a>1 do
  a:=a mod 2:
  count:=count+1:
 od:

if count mod 2=0 then
 L:=[op(L),2^count]:
 st:=st-2^count:
else
 L:=[op(L),2^(count-1)]:
 st:=st-2^(count-1):
fi:

od:
if st=1 then
 L:=[op(L),1]:
fi:
L:
end: