[May sure to write these problems up separately, since I might only collect one. -Prof. K.] /------------------------------------------------------------\ / \ Please carefully read all of NZM5.4 and the beginning of 5.5. Q4: Please solve NZM239#2. [Hint: First show that x is odd, then determine the parity of y.] Q5: Please solve this version of NZM239#4: For each even integer E, consider the Diophantine eqn. 1(E): x²+y²+z² = E·x·y·z. PROVE that the ONLY solution is the trivial one, x=y=z=0. Break your argument up into meaningful lemmata. [Hint1: If at least one of x,y,z is odd, establish that there is *no* solution, by working mod-[WHAT?].] [Hint2: Now use an "infinite descent" argument. The argument might change the value of E ... but no matter!] \ / \____________________________________________________________/