[May sure to write these problems up separately, since I might
only collect one. -Prof. K.]
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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!]
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