math.integer — integer-specific mathematics functions¶

This module provides access to the mathematical functions defined for integer arguments.These functions accept integers and objects that implement the__index__() method which is used to convert the object to an integernumber.

The following functions are provided by this module. All return values arecomputed exactly and are integers.

math.integer.comb(n,k,/)¶

Return the number of ways to choosek items fromn items without repetitionand without order.

Evaluates ton!/(k!*(n-k)!) whenk<=n and evaluatesto zero whenk>n.

Also called the binomial coefficient because it is equivalentto the coefficient of k-th term in polynomial expansion of(1+x)ⁿ.

RaisesValueError if either of the arguments are negative.

math.integer.factorial(n,/)¶

Return factorial of the nonnegative integern.

math.integer.gcd(*integers)¶

Return the greatest common divisor of the specified integer arguments.If any of the arguments is nonzero, then the returned value is the largestpositive integer that is a divisor of all arguments. If all argumentsare zero, then the returned value is0.gcd() without argumentsreturns0.

math.integer.isqrt(n,/)¶

Return the integer square root of the nonnegative integern. This is thefloor of the exact square root ofn, or equivalently the greatest integera such thata² ≤ n.

For some applications, it may be more convenient to have the least integera such thatn ≤ a², or in other words the ceiling ofthe exact square root ofn. For positiven, this can be computed usinga=1+isqrt(n-1).

math.integer.lcm(*integers)¶

Return the least common multiple of the specified integer arguments.If all arguments are nonzero, then the returned value is the smallestpositive integer that is a multiple of all arguments. If any of the argumentsis zero, then the returned value is0.lcm() without argumentsreturns1.

math.integer.perm(n,k=None,/)¶

Return the number of ways to choosek items fromn itemswithout repetition and with order.

Evaluates ton!/(n-k)! whenk<=n and evaluatesto zero whenk>n.

Ifk is not specified or isNone, thenk defaults tonand the function returnsn!.

RaisesValueError if either of the arguments are negative.