gcd or igcd denotes the gcd (greatest common divisor)
of several integers (for polynomials, see also 5.30.7).
gcd or igcd returns the GCD of integers.
Input:
Output:
Input:
Output:
Input:
Output:
We can also put as parameters two lists of same size (or a matrix with 2
rows), in this case gcd returns the greatest common divisor of
the elements with same index (or in the same column).
Input:
or:
Output:
An example
Find the greatest common divisor of 4n+1 and 5n+3 when n ∈ ℕ.
Input:
Then, input:
essai(n):={
local j,a,L;
L:=NULL;
for (j:=-n;j<n;j++) {
a:=f(j);
if (a!=1) {
L:=L,[j,a];
}
}
return L;
}
Then, input:
Output:
So we now have to prove that:
If n≠5+k*7 (for k ∈ ℤ), 4n+1 and 5n+3 are mutually prime,
and n=5+k*7 (for k ∈ ℤ), then the greatest common divisor of 4n+1
and 5n+3 is 7.