#include <stdio.h>

#define N 100

long max(long a, long b) { return a > b ? a : b; }
bool even(long i) { return i % 2 == 0; }
long gcd(long a, long b)
{
    while (b != 0)
    {
        long c = a % b;
        a = b;
        b = c;
    }
    return a;
}

long factors[N];
int nr_factors;

void analyse(long ai, long bi, long aj, long bj, long n)
{
    printf(" %2ld %2ld %2ld %2ld ", ai, bi, aj, bj);
    long c = (ai + aj)/2;
    long d = (aj - ai)/2;
    long e = (bi + bj)/2;
    long f = (bi - bj)/2;
    printf(" %3ld %3ld %3ld %3ld  %s", f, d, c, e,
           f < d && d <= c && c < e ? "" : "Error");
    long q = gcd(d, f);
    long r = gcd(c, e);
    long s = f/q;
    long t = d/q;
    printf("%3ld %3ld %3ld %3ld  %4ld %4ld = %4ld",
           q, r, s, t, (q*q + r*r), (s*s + t*t), (q*q + r*r)*(s*s + t*t));
    if ((q*q + r*r)*(s*s + t*t) != n)
        printf(" ERROR");
    else
    {
        long factor = (q*q + r*r) < (s*s + t*t) ? (q*q + r*r) : (s*s + t*t);
        int i;
        for (i = 0; i < nr_factors; i++)
            if (factors[i] == factor)
                break;
        if (i == nr_factors)
            factors[nr_factors++] = factor;
    }
    printf("\n");
}

int main(int argc, char *argv[])
{
    for (long n = 25; n <= 1000000; n += 2)
    {
        long as[N];
        long bs[N];
        long a = 0;
        long b = 1;
        while (b * b + a * a < n)
            b++;
        
        long c = 0;
        long g = 0;
        while (a < b)
        {
            if (b * b + a * a == n)
            {
                as[c] = a;
                bs[c] = b;
                if (g == 0)
                    g = gcd(a, b);
                else
                    g = gcd(g, gcd(a, b));
                c++;
            }
            a++;
            while (b * b + a * a > n)
                b--;
        }
        if (c >= 2 && g == 1)
        {
            printf("%ld ", n);
            for (long i = 0; i < c; i++)
                printf(" = %ld^2 + %ld^2", bs[i], as[i]);
            printf("\n");
            nr_factors = 0;
            for (long i = 0; i < c-1; i++)
                for (long j = i+1; j < c; j++)
                {
                    if (even(as[i]) == even(as[j]) && even(bs[i]) == even(bs[j]))
                        analyse(as[i], bs[i], as[j], bs[j], n);
                    if (even(as[i]) == even(bs[j]) && even(bs[i]) == even(as[j]))
                        analyse(as[i], bs[i], bs[j], as[j], n);
                }
            if (nr_factors != c-1)
                printf("Different %ld %ld %d %ld\n", n, c, nr_factors, g);
        }
    }
    return 0;
}