OFFSET
1,11
COMMENTS
For any integer n>=7, there exist integers x, y, z such that 0 <= x < n, 0 <= y < n, 0 <= z < n, n^2 = x^2 + y^2 - z^2. Hence the only functions f of the positive integers into themselves such that f(m^2+n^2) = f(m)^2 + f(n)^2 are the identity and the null function.
MATHEMATICA
r[n_] := Reduce[n^2 == x^2 + y^2 - z^2 && 0 <= x <= y < n && 0 <= z < n, {x, y, z}, Integers]; Reap[For[n = 1, n <= 100, n++, rn = r[n]; w = Which[rn === False, 0, Head[rn] === And, 1, Head[rn] === Or, Length[rn], True, -1; Print[n, " error"]]; Print[w]; Sow[w]]][[2, 1]] (* Jean-François Alcover, Jan 21 2016 *)
PROG
(Turbo-Pascal) VAR nMax, n, nbt, x, y, z: integer; BEGIN write('Maximum value of n: '); readln(nMax); for n := 1 to nMax do begin write(n, ':'); nbt := 0; for y := 0 to n-1 do for x := 0 to y do for z := 0 to n-1 do begin if x*x+y*y-z*z=n*n then begin nbt := nbt+1; write('(', x, ', ', y, ', ', z, ')'); end; end; writeln(' ', nbt, '.'); end; END.
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger Cuculière, Dec 10 2003
EXTENSIONS
More terms from Jean-François Alcover, Jan 21 2016
STATUS
approved