What is the value of ((131)39 + 11 ⋅ (-11))mod13 ? a. 3 b. 9 c. 10 d. 23

1. Solve 5x = 1(mod 19) 2. Use the EEA to find integers x and y such that: 300x + 222y = gcd(300,222) 3. Which of the following numbers are prime? Show why. a. 1527 b. 15277

23-2 Given a real number x, the expression is equivalent to: √√4+T O A. 1 22 OB. 1 2 C. 1 OD. 2 OE. 0

Bottled water and medical supplies are to be shipped to survivors ofan earthquake by plane. Each container of bottled water will serve 10 people and eachmedical kit will aid 6 people. Each plane can carry no more than 80,000 pounds. The bottledwater weighs 20 pounds per container and each medical kit weighs 10 pounds. Each planecan carry a total volume of supplies that does not exceed 6000 cubic feet. Each waterbottle is 1 cubic foot and each medical kit also has a volume of 1 cubic foot.   Thus, the maximum value of z is 36000 and this occurs when x = 0and y = 6000.In practical terms, this means that the maximum number of earthquake survivors whocan be helped with each plane shipment is 36000. This can be accomplished bysending 6000 medical kits.A) TrueB) False

Does ?2 ≡ 23 (mod 79) have any solutions. Justify your answer using the Legendre symbol.

Answer each of the following questions. ? 1. 23 = 56 mod 4 True 2. 24 = 154 mod 13 False 3. -4 = 4 mod 4 ? v 4. –5 = 62 mod 11 v 5. 7 = -29 mod 12

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The deciphering formula for C= (11P+16) mod 26 is ?