Special Quadratic Functions

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Special Quadratic Functions

• An Investigation

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• Special Quadratic Functions
• Consider the quadratic function ? f(n) n2
  n 41
• If we put n 0, we get f(0) 02 0 41 41
• If we put n 1, we get f(1) 12 1 41 43.
• Copy and complete the table below.
• What do you notice about the values of f(n)?
• What kind of special numbers are they?
• Is this type of number obtained for all values of
  n?
• Investigate.
• Try putting n 10, 15, 20, 25, 30, 35, 40,- -
  etc-

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• Exercise Make up a similar table of values for
  the function f(n) 2n2 29.
• What type of number does this formula generate?
• Can you find a quadratic formula which generates
  these special numbers, one after the other until
  it fails?

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• Solution
• The function f(n) n2 n 41 generates prime
• numbers for n 0,39.
• The numbers generated are called Euler numbers.
• Other quadratic prime generators include