 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Bifonacci (Posted on 2019-02-19) How many pairs of Fibonacci numbers each less than than 108 have a greatest common divisor equal to 233?

 No Solution Yet Submitted by Danish Ahmed Khan No Rating Comments: ( Back to comment list | You must be logged in to post comments.) re: Solution; also an extension Comment 2 of 2 | (In reply to Solution by Jer)

63245986 is F39, not F52.

F52 =  32951280099   =   3 * 233 * 521 * 90481

Its presence of a factor of 521 prevents its having a GCD of 233 with F26 but it does have such with both F13 and F39.

13 233
26 121393
39 63245986
52 32951280099

233 121393
233 63245986
233 32951280099
121393 63245986
63245986 32951280099

a = 1: b = 1: c = 2
Do
d = b + c
a = b: b = c: c = d
ct = ct + 1
fib(ct) = d
q = Int(d / 233): r = q * 233 - d
If r = 0 Then Text1.Text = Text1.Text & ct + 3 & Str(d) & crlf
Loop Until ct = 100 Or d > 10000000000000#

Text1.Text = Text1.Text & crlf

For i = 1 To ct - 1
For j = i + 1 To ct
If gcd(fib(i), fib(j)) = 233 Then Text1.Text = Text1.Text & fib(i) & Str(fib(j)) & crlf
Next
Next

Function gcd(a, b)
x = a: y = b
Do
q = Int(x / y)
z = x - q * y
x = y: y = z
Loop Until z = 0
gcd = x
End Function

Edited on February 19, 2019, 11:24 am
 Posted by Charlie on 2019-02-19 11:06:49 Please log in:

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