Sum of Two Squares

[Eddie W. Shore]

(08-17-2019 07:05 PM)klesl Wrote:  Very interesting :-)
Another interesting topic in number theroy is Bézout's_identity
https://en.wikipedia.org/wiki/Bézout's_identity
Can you write a program for this also?

Here is the Bezout program: this program returns the gcd of two integers a and b, and all of the possible integer solutions that fit a*x + b*y = d, with in a given range [-m, m]:

Code:

EXPORT BEZOUT(a,b,m)
BEGIN
// integers a, b, range -m to m
// 2019-08-19 EWS
LOCAL d,l,k,x,y;
d:=gcd(a,b);
l:={};
FOR k FROM −m TO m DO
x:=k;
y:=(d-a*x)/b;
IF FP(y)==0 THEN
l:=CONCAT(l,(x,y));
END;
END;
RETURN {d,l};
END;

Output: { gcd, list of (x,y) pairs }

Example: a = 18, b = 45, m = 20, find all solutions within the range [-20, 20]:
BEZOUT(18, 45, 20):

{9, {(-17, 7), (-12,5), (-7,3), (-2,1), (3,-1), (8,-3), (13,-5), (18,-7)}}