greatest common divisor test (GCD test) is the test used in study of loop optimization and loop dependence analysis to test the dependency between loop...

(1 < gcd(a,n) < n for some a ≤ r), output composite. For (a = r; a > 1; a--) { If ((gcd = GCD[a,n]) > 1 && gcd < n), Return[Composite] } gcd = {GCD(29,31)=1...

multiple tests. If two (successful) strong probable prime tests find x2 ≡ −1 (mod n) and y2 ≡ −1 (mod n), but x ≢ ±y (mod n), then gcd(x − y, n) and gcd(x +...

common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that a x + b y = gcd ( a , b ) . {\displaystyle...

that i is a divisor for j; and gcd is the greatest common divisor. Note: Equation (1) is simply a Fermat primality test. If we find any value of a, not...

{\displaystyle \gcd(2u,2v)=2\cdot \gcd(u,v)} : 2 {\displaystyle 2} is a common divisor. gcd ( u , 2 v ) = gcd ( u , v ) {\displaystyle \gcd(u,2v)=\gcd(u,v)} if...

Euler–Jacobi pseudoprime. When n is odd and composite, at least half of all a with gcd(a,n) = 1 are Euler witnesses. We can prove this as follows: let {a1, a2,...

for which all values of a {\displaystyle a} with gcd ⁡ ( a , n ) = 1 {\displaystyle \operatorname {gcd} (a,n)=1} are Fermat liars. For these numbers, repeated...

algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that divides them both without a remainder...

The GCD is a commutative function: gcd(a, b) = gcd(b, a). The GCD is an associative function: gcd(a, gcd(b, c)) = gcd(gcd(a, b), c). Thus gcd(a, b,...

their GCD. gcd ( p , q ) = gcd ( q , p ) . {\displaystyle \gcd(p,q)=\gcd(q,p).} gcd ( p , q ) = gcd ( q , p + r q ) {\displaystyle \gcd(p,q)=\gcd(q,p+rq)}...

: gcd ( x , y ) = gcd ( y , x % y ) {\displaystyle \gcd(x,y)=\gcd(y,x\%y)} if y ≠ 0 {\displaystyle y\neq 0} gcd ( x , 0 ) = x {\displaystyle \gcd(x,0)=x}...

statements must be executed in order of their (potential) true dependence. GCD test Randy Allen and Ken Kennedy. Optimizing Compilers for Modern Architectures:...

k = gcd ⁡ ( a − c , d − b ) {\displaystyle k=\operatorname {gcd} (a-c,d-b)} and h = gcd ⁡ ( a + c , d + b ) {\displaystyle h=\operatorname {gcd} (a+c...

graphics card to be based on a chiplet design TSMC N5 for Graphics Compute Die (GCD) TSMC N6 for Memory Cache Die (MCD) Up to 24 GB of GDDR6 video memory Doubled...

Lehmer's GCD algorithm, named after Derrick Henry Lehmer, is a fast GCD algorithm, an improvement on the simpler but slower Euclidean algorithm. It is...

algorithm in base n > 1: gcd ( n a − 1 , n b − 1 ) = n gcd ( a , b ) − 1. {\displaystyle \gcd \left(n^{a}-1,n^{b}-1\right)=n^{\gcd(a,b)}-1.} A set of integers...

compute gcd ( N , a r / 2 + 1 ) {\displaystyle \gcd(N,a^{r/2}+1)} ; it will produce a nontrivial factor if gcd ( N , a r / 2 − 1 ) {\displaystyle \gcd(N,a^{r/2}-1)}...

Alternatively, any number Q = 10c + d is divisible by n = 10a + b, such that gcd(n, 2, 5) = 1, if c + D(n)d = An for some integer A, where D ( n ) ≡ { 9 a...

{p}}+1\right)^{2}\leq \left({\sqrt[{4}]{N}}+1\right)^{2}<q} and thus gcd ( q , m p ) = 1 {\displaystyle \gcd(q,m_{p})=1} and there exists an integer u with the property...

calculation of the gcd ( v , n ) {\displaystyle \gcd(v,n)} . Assuming we calculate a slope of the form u / v {\displaystyle u/v} with gcd ( u , v ) = 1 {\displaystyle...

n ) = { 0 if  gcd ( a , n ) ≠ 1 , ± 1 if  gcd ( a , n ) = 1. {\displaystyle \left({\frac {a}{n}}\right)={\begin{cases}0&{\text{if }}\gcd(a,n)\neq 1,\\\pm...

Alternately, any number p satisfying the equality gcd ( p , ∑ a = 1 p − 1 a p − 1 ) = 1 {\displaystyle \gcd \left(p,\sum _{a=1}^{p-1}a^{p-1}\right)=1} is...

test whether gcd ( e , p − 1 ) = 1 {\displaystyle \gcd(e,p-1)=1} and gcd ( e , q − 1 ) = 1 {\displaystyle \gcd(e,q-1)=1} while generating and testing...

Brent. They observed that if gcd ( a , n ) > 1 {\displaystyle \gcd(a,n)>1} , then also gcd ( a b , n ) > 1 {\displaystyle \gcd(ab,n)>1} for any positive...

Factors with deg(u) > d do if gcd(g, u) ≠ 1 and gcd(g, u) ≠ u, then Factors:= Factors ∖ { u } ∪ { ( gcd ( g , u ) , u / gcd ( g , u ) ) } {\displaystyle...

being GCD(b ± 1, p). b2 ≠ 1, where p is proven composite by Fermat's test, base a. b = 0, where p has a nontrivial divisor GCD(a, p). Where GCD(x, y)...

lower yields. RDNA 3 uses two types of chiplets: the Graphics Compute Die (GCD) and Memory Cache Dies (MCDs). On Ryzen and Epyc processors, AMD used its...

rapidly checked without having to run an expensive or unreliable primality test. "Succinct" usually means that the proof should be at most polynomially larger...

Provided GCD(n, Q) = 1 then testing for congruence (4) is equivalent to augmenting our Lucas test with a "base Q" Solovay–Strassen primality test. There...