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<DIV><FONT face=Arial size=2>Define</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2> f(1) = 1</FONT></DIV>
<DIV><FONT face=Arial size=2> f(n+1) = f(n) + (f(n) mod
n+3364).</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I wrote a computer program to find the smallest x
with</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2> x+3365 divides f(x)</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>The value of x found is just under 8,350,000,000
and the corresponding f(x) just under 2^64. Although my program included an
overflow check, I am still not comfortable because this value of f(x) is close
to my 64-bit unsigned integer size.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Could someone with a fast computer, preferably a
UNIX box, please confirm or refute my values?</FONT></DIV></BODY></HTML>