1, 1, 0, Go!

Computer Science Level pending

9227465 5702887 3524578 5 3 2 1 1 0 \large { {9227465 \, 5702887 \, 3524578 \ldots 5 \, 3 \, 2 \, 1 \, 1 \, 0} }

The above expression shows the concatenation of the Fibonacci numbers less than or equal to 1 0 7 10^7 written backwards.

Let L L and S S denote the number of digits and the sum of digits, respectively, of this large number. What can you say about the number obtained from the expression given below? 1 10 [ ( S L ) ( m o d 2016 ) ] \dfrac1{10} \left[ (S-L) \pmod{2016} \right]

It is an even number It is a perfect square It is a multiple of 5 It is a prime number

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

展豪 張
Mar 15, 2016

>> a='0'
>> b=c=1
>> while b<10**7:a,b,c=str(b)+a,c,b+c

>> a
'922746557028873524578217830913462698320405142293178111964181213937502546368286571771110946676541812584159798761037723314489553421138532110'
>> len(a)
138
>> sum(map(int,a))
592

The number is 45.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...