1, 1, 0, Go!

Computer Science Level pending

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

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

Let $L$ and $S$ 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? $\dfrac1{10} \left[ (S-L) \pmod{2016} \right]$

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

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.

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