a. If the pseudo-Fibonacci numbers are defined by u(1) = 1 , u(2) = 4, u(n)= u(n-1)+u(n-2) show that u(1) = 1, u(2) = 4, and u(4) = 9 are the only squares in the series.

b. How many ordered integer pairs (a,b) both non-negative (a<b) exist, such that a pseudo-Fibo series based upon any of those pairs (i.e. u(1)=a, u(2)=b... etc) will contain 520 as a member generated by that pair ?

One might also consider as solutions
a=1, b=520
a=2, b=520
etc.
as the pseudo-Fibo series does contain 520 as its second term.
Also a=520, any b>520 contains 520 as its first term.
I understand this is not the intent of the problem but it seems a reasonable interpretation of 'generated' to me. 

That's why I earlier suggested specifying a<b<520.
(Which only removes a=0, b=520 from Charlie's list.)

Posted by Jer on 2014-04-15 00:06:58