# HW 2
# OK to post

Help := proc(): 
print(`binomCoeff(n), nopsTest(n)`): 
end:

# outputs the binomial coefficients of N-th degree
binomCoeff := proc(N) local s,j, i,y:
s:= 1:
if N<0 then
 RETURN(FAIL):
fi:

if N=0 then #not sure how to return multiple lines yet
 RETURN(s):
fi:

for i from 1 to N do
 s := 0,s,0;
 y := seq(s[j]+s[j+1], j=1..i+1):
 s:= y:
od:
y:
end:

nops([1,2,4]);
nops([2,780]);

nopsTest := proc(N):
 nops([binomCoeff(N)]);
end:	

M:= table([
january = 1,
february = 2,
march = 3,
april = 4,
may = 5,
june = 6,
july = 7,
august = 8,
september = 9,
october = 10,
november = 11,
december = 12
]);

M[january];
M[march];                   
M[december];

type(M, table);
type([binomCoeff(3)],list);

with(NumberTheory):

# Euler Theorem verification (exercise 1)
gcd(10^90,10^90-1);
a:=10^90;
n:=10^90 - 1;
a&^phi(n) mod n;

# Exercise 2
p:=ithprime(10^3);
q:=ithprime(10^4+28);
n:=p*q;
e:=ithprime(10^5+29);
gcd(phi(n),e);

d:=e&^(-1) mod phi(n);