Help:=proc(): print(`BestNei2(f,a,b,a0,b0),FindLC(f,a,b,a0,b0`):
print(`Pell1(K)`):
end:

#BestNei2(f,a,b,a0,b0): inputs an expression f in the
#symbols a,b, and integers a0,b0 and outputs
#[a0,b0] if f(a0,b0) is smaller than its neighbors
#otherwise [a1,b1], where f(a1,b1) is the `smallest neighbor'
#and the new record
BestNei2:=proc(f,a,b,a0,b0) local champ,Neis,a1,b1,rec,i:

Neis:={[a0+1,b0],[a0-1,b0],[a0,b0-1],[a0,b0+1]}:


champ:=[a0,b0]:
rec:=subs({a=a0,b=b0},f):

for i from 1 to nops(Neis) do
   
   a1:=Neis[i][1]: b1:=Neis[i][2]:

     if a1>0 and b1>0 then
       if subs({a=a1,b=b1},f)<rec then
            champ:=[a1,b1]:
         rec:=subs({a=a1,b=b1},f):
        fi:
      fi:
od:
champ,rec:
end:

 
FindLC:=proc(f,a,b,a0,b0) local champ,rec,NewChamp,Newrec:

champ:=[a0,b0]: 
NewChamp:=BestNei2(f,a,b,a0,b0)[1]:

while NewChamp<>champ do
  champ:=NewChamp:
  NewChamp:=BestNei2(f,a,b,op(NewChamp))[1]:
od:
champ,BestNei2(f,a,b,op(champ))[2]:


end:



#inputs an integer K and outputs all solutions [a,b]
#of a^2-2*b^2=1 in 1<=a<b<=K
Pell1:=proc(K) local S,a,b:

S:=[]:
for a from 1 to K do
  b:=sqrt((a^2-1)/2):
       if type(b,integer) and b>1 then
        S:=[op(S),[a,b]]:
      fi:
  
 b:=sqrt((a^2+1)/2):
       if type(b,integer) and b>1 then
        S:=[op(S),[a,b]]:
      fi:
od:
S:
end:


#Inputs K and and outputs all the triplets [a,b,c]
#such that (a^3+b^3-c^3) =\pm 1
Wiles3:=proc(K)
local a,b,c,S:

end: