Reference no: EM131569059

Question: [BB] It is tempting to think that if a statement involving the natural number n is true for many consecutive values of n, it must be true for all n. In this connection, the following example due to Euler is illustrative. Let f(n) = n² +n+41.

(a) Convince yourself (perhaps with a computer algebra package like Maple or Mathematica) that f(n) is prime for n = 1, 2, 3, ... 39 but that f(40) is not prime.

(b) Show that for any n of the form n = k² + 40, f (n) is not prime.