Question: 10. Find a7 for the sequence with generating function 2 (1 - x)2 1-2-22 Hint You should multiply the two sequences. 2. Suppose a, b,

10. Find a7 for the sequence with generating function 2 (1 - x)2 1-2-22 Hint You should "multiply" the two sequences. 2. Suppose a, b, and c are integers. Prove that if a | b and a | c then a | b + c and a b - c. 4. What is the largest n such that 16 and 25 are in the same remainder class modulo n? Write out the remainder class they both belong to and give an example of a number more than 100 in that class. 8. Determine which of the following congruences have solutions, and find any solutions (between 0 and the modulus) by trial and error. a. 4x = 5 (mod 6). b. 6x = 3 (mod 9). c. x2 = 2 (mod 4)

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