[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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