Question

Prove that n^2-n+41 is prime by induction

Answer 1

Answer:

Let us denote the statement by s:n^2-n+41 is a prime number.

For n=1,s(1)=1^1-1+41=41 which is a prime number.

Let the statement be true for n=k also, then s(k) =k^2-k+41 is also a prime number.

Now, for n=k+1,we have

S(k+1)=(k+1)^2-(k+1)+41

=k^2+2k+1-k-1+41

=k^2+k+41

=k^2-k+41+2k

=a prime number(m) +2k

But,the statement is itself prime for the value k

So, s(k+1) is also prime

Hence showed