/**
* Compute the primitive part and the content of a modular multivariate
* polynomial e \in Z_p[x_n][x_0, \ldots, x_{n-1}], i.e. e is considered
* a polynomial in variables x_0, \ldots, x_{n-1} with coefficients being
* modular polynomials Z_p[x_n]
* @param e polynomial to operate on
* @param pp primitive part of @a e, will be computed by this function
* @param c content (in the sense described above) of @a e, will be
* computed by this function
* @param vars variables x_0, \ldots, x_{n-1}, x_n
* @param p modulus
*/
void primpart_content(ex& pp, ex& c, ex e, const exvector& vars,
const long p)
{
static const ex ex1(1);
static const ex ex0(0);
e = e.expand();
if (e.is_zero()) {
pp = ex0;
c = ex1;
return;
}
exvector rest_vars = vars;
rest_vars.pop_back();
ex_collect_t ec;
collect_vargs(ec, e, rest_vars);
if (ec.size() == 1) {
// the input polynomial factorizes into
// p_1(x_n) p_2(x_0, \ldots, x_{n-1})
c = ec.rbegin()->second;
ec.rbegin()->second = ex1;
pp = ex_collect_to_ex(ec, rest_vars).expand().smod(numeric(p));
return;
}
// Start from the leading coefficient (which is stored as a last
// element of the terms array)
auto i = ec.rbegin();
ex g = i->second;
// there are at least two terms, so it's safe to...
++i;
while (i != ec.rend() && !g.is_equal(ex1)) {
g = euclid_gcd(i->second, g, vars.back(), p);
++i;
}
if (g.is_equal(ex1)) {
pp = e;
c = ex1;
return;
}
exvector mainvar;
mainvar.push_back(vars.back());
for (i = ec.rbegin(); i != ec.rend(); ++i) {
ex tmp(0);
if (!divide_in_z_p(i->second, g, tmp, mainvar, p))
throw std::logic_error(std::string(__func__) +
": bogus division failure");
i->second = tmp;
}
pp = ex_collect_to_ex(ec, rest_vars).expand().smod(numeric(p));
c = g;
}
int main(int argc, char *argv[])
{
int primes[168] = {
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
};
int t = gint();
int i, a, b, gcd, ans, tmp;
while(t--){
a = gint();
b = gint();
gcd = euclid_gcd(a, b);
ans = 1;
for (i = 0; i < 168; ++i)
{
if (gcd <= 1)
break;
tmp = 0;
while(!(gcd % primes[i])){
gcd /= primes[i];
tmp++;
}
ans *= tmp + 1;
}
if(gcd > 1)
ans *= 2;
pint(ans);
putchar_unlocked('\n');
}
return 0;
}
