Number Theory Functions

• GCD
  GCD calculates the greatest common divisor of two values.

Example:

98
[GCD]
140
[ENTER]
Displays: 14

• conjg
  Complex conjugate. It operates in a postfix manner and returns the conjugate of a complex value.

For example:

5 [;] 6
[ENTER]
Displays: 5 + 6i
[conjg]
Displays: 5 - 6i

It does nothing in base-N modes or if use of complex numbers is disabled.

• FRCPT
  Fractional part. Returns the fraction part of a value.

For example:

5.23237
[FRCPT]
Displays: 0.23237

Note. This function always operates in a postfix manner on the calculator window, but should be used prefix with the Function Grapher.

• HEAVY
  Accepts a single value, and returns 0 if the value is less than or equal to zero, or +1 otherwise.

Note. This function is available from the [MISC] menu key, but its real value lies in its use with the Function Grapher.

• IMGPT
  Imaginary part. It operates in a postfix manner and returns the imaginary component of a complex value.

For example:

5 [;] 6
[ENTER]
Displays: 5 + 6i
[IMGPT]
Displays: 6

It does nothing in base-N modes or if use of complex numbers is disabled.

• INTPT
  Integer part. Returns the integer part of a value.

Example:

5.23237
[INTPT]
Displays: 5

Note. This function always operates in a postfix manner on the calculator window, but should be used prefix with the Function Grapher.

• LCM
  LCM calculates the least common multiple of two values.

Example:

5
[LCM]
3
[ENTER]
Displays: 15

• MISC
  The [MISC] key provides a menu input for a range of miscellaneous functions.
• MOD
  MOD returns the modulo value of the first argument with respect to the second. It is defined as the amount by which the first argument exceeds the largest integer multiple of the divisor that is not greater than that number.

Example:

27.87
[MOD]
12
[ENTER]
Displays: 3.87

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Info: MOD is sometimes incorrectly referred to as the "remainder function"--where both arguments are positive the result will indeed be the remainder, but not for negative values. If you wish to calculate the remainder rather than modulus, use the REM function in base-N mode.

• nCr
  Calculates the number of ways of picking r unordered outcomes from n possibilities.

Example: Determine how many 3 member groups can be organized in a group of 12 individuals.

12 [nCr] 3
[ENTER]
Displays: 220

• nPr
  Calculates the number of ways of obtaining an ordered subset of r elements from a set of n elements.

Example: Determine how many 4 digit values can be produced using the numbers 1 to 16.

16 [nPr] 4
[ENTER]
Displays: 43680

• PRIME
  PRIME is available from the [MISC] function key. It uses the Sieve of Eratosthenes method to determine the nth prime, beginning with PRIME(1) = 2. The larger the value of n, the longer the time required to determine the result. Therefore, this function places an upper time limit on the calculation, and returns a Timeout error if the result cannot be determined in this time. This upper limit is configurable, and can be set with the 'Timeout' option in the configuration settings. Note that this function is not designed to generate huge primes and it will, therefore, return Range Error if the input value exceeds 20E6. Generally, however, a computer with a 2GHz CPU should be able to determine the millionth prime number within around 2 seconds.

Example: What is the millionth prime number?

[PRIME] 1E6
[ENTER]
Displays: 15485863

• PRIMEQ
  PRIMEQ is available from the [MISC] function key. It returns +1 is the input value is prime, or zero otherwise.
• Ran#
  Returns a pseudo random number n, where n will be in the range, 0 <= n < 1.

For example, to generate a random number between 1 and 47 inclusive, enter:

1 [+] Ran# [×] 47
[ENTER]
Displays: 17.187... (result is variable)

Ran# takes no input parameter.

• REALPT
  Real part. Returns the real component of a complex value.

For example:

5 [;] 6
[ENTER]
Displays: 5 + 6i
[REALPT]
Displays: 5

It does nothing in base-N modes or if use of complex numbers is disabled.

• SIGN
  Accepts a single value, and returns -1 if the value is below 0, zero if the input is zero, or +1 if greater than zero.

Note. This function is available from the [MISC] menu key, but its real value lies in its use with the Function Grapher.