Rating: 5.0

# Crunchy - 50 points - 73 solves
# Binary recurrence sequence modulo prime

We get a recurrence relation x(n) = 6*x(n-1)+x(n-2), with x(0)=0,x(1)=1. The flag is INSA{x(g)%p} for a very large value of g and a prime p.

This challenge is trivial to solve using a module of sage I discovered: sage.combinat.BinaryReccurenceSequence. With this module we can easily find the period of x modulo p. Then we just need to reduce g modulo this period and we get the flag. Here is the solution script:
python
p = 100000007
T = BinaryRecurrenceSequence(6,1)
period = T.period(p)
g = 17665922529512695488143524113273224470194093921285273353477875204196603230641896039854934719468650093602325707751568
trunc_g = g%period
print T(trunc_g)%p

which gives the flag INSA{41322239}.