maths Maths Puzzle

The terms of a sequence of positive integers satisfy an+3 = an+2(an+1 + an), for n = 1, 2, 3, ... .
If a6 = 8820, what is a7?

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maths Other Question

Let n be a positive integer. Prove that n! + 1 is composite for infinitely many values of n. Show that, for all integers m and n, mn(m420 − n420) is divisible by 446617991732222310.