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55 lines
1.2 KiB
Plaintext
55 lines
1.2 KiB
Plaintext
NAME
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gcdrem - result of removing factors of integer common to a specified integer
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SYNOPSIS
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gcdrem(x, y)
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TYPES
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x integer
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y integer
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return non-negative integer
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DESCRIPTION
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If x and y are not zero, gcdrem(x, y) returns the greatest integer
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divisor d of x relatively prime to y, i.e. for which gcd(d,y) = 1.
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In particular, gcdrem(x,y) = abs(x) if x and y are relatively
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prime.
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For all x, gcdrem(x, 0) = 1.
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For all nonzero y, gcdrem(0, y) = 0.
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PROPERTIES
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gcdrem(x,y) = gcd(abs(x), abs(y)).
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If x is not zero, gcdrem(x,y) = gcdrem(x, gcd(x,y)) = gcdrem(x, y % x).
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For fixed nonzero x, gcdrem(x,y) is periodic with period abs(x).
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gcdrem(x,y) = 1 if and only if every prime divisor of x
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is a divisor of y.
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If x is not zero, gcdrem(x,y) == abs(x) if and only if gcd(x,y) = 1.
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If y is not zero and p_1, p_2, ..., p_k are the prime divisors of y,
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gcdrem(x,y) = frem(...(frem(frem(x,p_1),p_2)...,p_k)
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EXAMPLE
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> print gcdrem(6,15), gcdrem(15,6), gcdrem(72,6), gcdrem(6,72)
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2 5 1 1
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> print gcdrem(630,6), gcdrem(6,630)
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35 1
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LIMITS
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none
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LIBRARY
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NUMBER *qgcdrem(NUMBER *x, NUMBER *y)
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SEE ALSO
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gcd, frem, isrel
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