Question 4) Let

p>2

be a prime. A solution

x,y,z

of the equation

x^(p)+y^(p)=z^(p)

is said to be case 1\ if

p

does not divide

x,y

and

z

. Show that the equation

x^(3)+y^(3)=z^(3)

does not have any case 1 solution.\ Hint: Consider the equation modulo 9.

Question 4) Let p>2 be a prime. A solution x,y,z of the equation xp+yp=zp is said to be case 1 if p does not divide x,y and z. Show that the equation x3+y3=z3 does not have any case 1 solution. Hint: Consider the equation modulo 9