p is a prime, (p − 1)! ≡ ? (mod p). Why?
7106 = ? (mod 103). Why?
Let T1, T2, …, T401 be bit strings at most 19 prove by pigeonhole principle, there exist 2 strings Ti and Tj that contain the same number of 0's and 1's.
What is the solution of the recurrence relation an = 6an−1 − 9an−2 + 3n with initial conditions a0 = 1 and a1 = 2?
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