kill(all);

van=facebook.com/LearningCalculus$

      Problem 2:
      f(x):=   0 is one       solution
      f(x):= x-1 is the other solution
      No solutions in polynomials x^(n  ) where n > 1 exist
      No solutions in functions   x^(1/n) where n > 1 exist

f(x):=0$

g(x,y):=f(f(x)*f(y))+f(x+y) = f(x*y);

fullratsimp(g(x,y));

f(x):=x-1$

ratsimp(g(x,y));

f(x):=x^n$

ratsimp(g(x,y));

f(x):=x^(1/n);

ratsimp(g(x,y));

Problem 1:

is(integerp(4));

is(integerp(%pi));

if true then "yes" else "no";

a0: 5$

create_list(if is(integerp(sqrt(i))) then 1 else 0, i, a0, 26);

create_list(if is(integerp(sqrt(i))) then sqrt(i) else i+3, i, a0, 22);

an:last(%);