Thread: Sequence
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Old 2005-09-14, 13:07   #3
Jushi
 
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Sep 2005
UGent

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Let T = t(1). Then:
t(2) = T + 1
t(3) = t(2)*t(1) + 1 = (T + 1)*T + 1 = T^2 + T + 1
t(4) = t(3)*t(2)*t(1) + 1 = (T^2 + T + 1)*(T + 1)*T + 1 = T^4 + 2T^3 + 2T^2 + T + 1

By looking modulo 5, the condition that t(4) is divisible by 5 is impossible.
The best sequence is thus:
t(1) = 1
t(2) = 2
t(3) = 3
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