x_1 = 1;

x_n = 1/2 (x_n-1 + 3/x_n-1 ) for n>=2

Is there a maple command to check if the above statement is rational, eventhough it is obvious enough?

I tried to evaluate x_2 using subs(n=2, x_n) but keep getting an expression in terms of x_1. Using evalf(x_2), the result was x_2.

I'm very new to maple, so please help :(

How do I use msolve to solve y^2 + y - 11=0 in Zp for all primes p with 41=< p =<107 ?

Also, using the results make a conjecture describing the primes p for which there are solutions to y^2 + y - 11 = 0 in Zp

This was what I did.

41<=p<=107

msolve(y^2 + y - 11=0, p)

but I received this error, no implementation of msolve matches the arguments in call, msolve(y^2 + y - 11=0, p)

Any help is appreciated. Thanks

Nm= p1.
p2 ...pm + 1, for m more than or equals 1.

So N1 = p1 + 1 = 2 + 1 = 3, N2 = p1 p2 + 1 = 2
3 + 1 = 7, etc.

We prove that Nm is not divisible by any of p1, p2, . . . , pm, so that Nm is either a prime or it is divisible by a prime larger than pm.

(c) Use Maple to find out which of these numbers Nm, for m = 1, 2, . . . , 15, is actually prime.

Use Maple to compare pm with the smallest prime number that divides Nm, for m =1, 2, . . . , 15.