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This section will cover the Integer commands of the HP Prime. Unless noted, the commands are practically useful only in CAS Mode and in CAS programs.
Examples given in this section is with the CAS Simplify setting set to Maximum. The “Include complex results in variables” option is turned off.
Returns a sequence (vector) of an integer's divisors.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
idivis(integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.idivis(integer)
Home Mode - RPN Entry:
1: integer CAS.idivis(1) press Enter
Examples:
CAS Mode
idivis(36) returns [1 2 4 3 6 12 9 18 36]
Access: Toolbox, CAS, 5. Integers, 1. idivis
See Also: ifactor, lcm, gcd
Returns the prime factorization of an integer. The output is a textbook representation of an integer's factorization.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
ifactor(integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.ifactor(integer)
Home Mode - RPN Entry:
1: integer CAS.ifactor(1) press Enter
Examples:
CAS Mode
ifactor(36) returns 2^2*3^2
Access: Toolbox, CAS, 5. Integers, 2. ifactor
Note: Be careful because the commands ifactor and ifactors do different things (one little “s”).
See Also: idivis, ifactors
Returns the prime factorization of an integer. The output is a sequence of pairs: prime divisor followed by its multiplicity.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
ifactors(integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.ifactors(integer)
Home Mode - RPN Entry:
1: integer CAS.ifactors(1) press Enter
Examples:
CAS Mode
ifactors(36) returns [2 2 3 2]
Access: Toolbox, CAS, 5. Integers, 3. ifactors
Note: Be careful because the commands ifactor and ifactors do different things (one little “s”).
See Also: ifactor, isprime
Greatest common divisor of two polynomials or integers.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
Greatest Common Divisor of Polynomials:
gcd(polynomial, polynomial)
Greatest Common Divisor of Integers:
gcd(integer, integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.gcd(integer, integer)
Home Mode - RPN Entry:
2: integer
1: integer
CAS.gcd(2)
Examples:
CAS Mode
Polynomials:
gcd(2x^2+4x, 4x) returns 2x
gcd(2x^3+2, 3x^5+3) returns x+1
Integers:
gcd(175, 225) returns 25
Access:
Toolbox, CAS, 6. Polynomial, 5. gcd OR
Toolbox, CAS, 5. Integers, 5. gcd
See Also: lcm, euler
Least common multiple of two polynomials or integers.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
Least Common Multiple of Polynomials:
lcm(polynomial, polynomial)
Least Common Multiple of Integers:
lcm(integer, integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.lcm(integer, integer)
Home Mode - RPN Entry:
2: integer
1: integer
CAS.lcm(2)
Examples:
CAS Mode
Polynomials:
lcm(x+1, x^2-1) returns x^2-1
lcm(x^2+1, x^3-1) returns x^5+x^3-x^2-1
Integers:
lcm(175, 225) returns 1575
Access:
Toolbox, CAS, 6. Polynomial, 6. lcm OR
Toolbox, CAS, 5. Integers, 6. lcm
See Also: gcd
Tests to see if an integer is a prime number. The number is prime if the integer's divisors are only itself and 1.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
isprime(integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.isprime(integer)
Home Mode - RPN Entry:
1: integer CAS.isprime(1), press Enter
Output:
In CAS mode, isprime returns true and false.
In all other modes, CAS.isprime returns 1 (representing true) and 0 (representing false).
Examples:
CAS Mode
isprime(36) returns false
isprime(47) returns true
Home Mode
CAS.isprime(36) returns 0
CAS.isprime(47) returns 1
Access: Toolbox, CAS, 5. Integer, 6. Prime, 1. isprime
See Also: ifactor, ifactors
Returns the nth prime number. Example, ithprime(25) returns the 25th prime number, which is 97. The sequence of primes is: 2, 3, 5, 7, etc.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
ithprime(integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.ithprime(integer)
Home Mode - RPN Entry:
1: integer CAS.ithprime(1), press Enter
Note: If the argument for ithprime is not an integer, it returns an “Error: Bad Argument Type” .
Examples:
CAS Mode
ithprime(25) returns 97.
ithprime(36) returns 149.
Access: Toolbox, CAS, 5. Integer, 6. Prime, 2. ithprime
See Also: isprime, nextprime, prevprime
Returns the next prime number greater than n.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
nextprime(integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.nextprime(integer)
Home Mode - RPN Entry:
1: integer CAS.nextprime(1), press Enter
Note: If the argument for nextprime is not an integer, it returns an “Error: Bad Argument Type” .
Examples:
CAS Mode
nextprime(33) returns 37
nextprime(37) returns 41
Access: Toolbox, CAS, 5. Integer, 6. Prime, 3. nextprime
See Also: isprime, ithprime, prevprime
Returns the next prime number less than n.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
prevprime(integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.prevprime(integer)
Home Mode - RPN Entry:
1: integer CAS.prevprime(1), press Enter
Note: If the argument for prevprime is not an integer, it returns an “Error: Bad Argument Type” .
Examples:
CAS Mode
prevprime(33) returns 31
prevprime(31) returns 29
Access: Toolbox, CAS, 5. Integer, 6. Prime, 5. prevprime
See Also: isprime, ithprime, nextprime
Euler's phi function, also known as the totient function. Φ(n). The function returns the number of positive integers less than or equal to n which are coprime to n. An integer is coprime to n if their greatest common divisor (gcd) is 1.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
euler(integer)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.euler(integer)
Home Mode - RPN Entry:
1: integer CAS.euler(1), press Enter
Note: If the argument for euler is not an integer, it returns an “Error: Bad Argument Type” .
Examples:
CAS Mode
euler(25) returns 20
euler(36) returns 12
Access: Toolbox, CAS, 5. Integer, 6. Prime, 5. euler
See Also: gcd
Returns the quotient portion of the division m ÷ n, where m and n are integers.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
iquo(dividend or numerator, divisor or denominator)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.iquo(dividend or numerator, divisor or denominator)
Home Mode - RPN Entry:
2: dividend or numerator 1: divisor or denominator CAS.iquo(2), press Enter
Examples:
CAS Mode
iquo(96, 85) returns 1
iquo(96, 6) returns 16
Access: Toolbox, CAS, 5. Integer, 7. Division, 1. iquo
See Also: ÷, irem
Returns the remainder portion of the division m ÷ n, where m and n are integers.
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
irem(dividend or numerator, divisor or denominator)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.irem(dividend or numerator, divisor or denominator)
Home Mode - RPN Entry:
2: dividend or numerator 1: divisor or denominator CAS.irem(2), press Enter
Examples:
CAS Mode
irem(96, 85) returns 11
irem(96, 6) returns 0
Access: Toolbox, CAS, 5. Integer, 7. Division, 2. irem
See Also: ÷, iquo
Integer Chinese Remainder Theorem for two equations. Takes two lists [a, p] and [b, q] and returns a list of two integers [r, n] such that x Ξ r mod n. In this case, x Ξ a mod p, x Ξ b mod q, and n Ξ p * q.
Source: HP Prime help screen for ichinrem
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
ichinrem([a,p],[b,q])
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.inchinrem([a,p],[b,q])
Home Mode - RPN Entry:
2: [a, p]
1: [b, q]
CAS.inchinrem(2), press Enter
Examples:
CAS Mode
ichinrem([2,7],[3,5]) returns [-12, 35] meaning:
Access: Toolbox, CAS, 5. Integer, 7. Division, 3. inchinrem
See Also: ÷, irem
Power and modulo function. powmod takes three integers: a, n, and p and returns a^n mod p.
Source: HP Prime help screen for powmod
Syntax
Input:
CAS Mode
Program Editor - CAS Programs
powmod(a,n,p)
Home Mode- Algebraic or Textbook Entry:
Normal Program Editor
CAS.powmod(a,n,p)
Home Mode - RPN Entry:
3: a
2: n
1: p
CAS.powmod(3), press Enter
Examples:
CAS Mode
powmod(4,8,6) returns 4 (4^8 MOD 6)
powmod(8, 2,3) returns 1 (8^2 MOD 3)
Access: Toolbox, CAS, 5. Integer, 7. Division, 4. powmod
See Also: mod
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