Mathematics Contest University of South Carolina December 5, 1998
... 2. Four friends go fishing one day and bring home a total of 11 fish. If each person caught at least one fish, then which one of the following must be true? (a) Somebody caught exactly 2 fish. (b) Somebody caught exactly 3 fish. (c) Somebody caught fewer than 3 fish. (d) Somebody caught more than 3 ...
... 2. Four friends go fishing one day and bring home a total of 11 fish. If each person caught at least one fish, then which one of the following must be true? (a) Somebody caught exactly 2 fish. (b) Somebody caught exactly 3 fish. (c) Somebody caught fewer than 3 fish. (d) Somebody caught more than 3 ...
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Multiplying Integers
... Multiplying Integers • Multiply the absolute values of the integers. • If both integers have the same sign, the product is positive. • If they have different signs, the product is negative. ...
... Multiplying Integers • Multiply the absolute values of the integers. • If both integers have the same sign, the product is positive. • If they have different signs, the product is negative. ...
Parry A
... 6.5: We did what we need to do with congruence testing with right triangles already. We did the HL. This chapter also includes LL (SAS), HA and LA (both AAS). Pythagoreans: 1 represented logic because reason could produce only one consistent body of truths 2 stood for man 3 stood for woman 4 stood f ...
... 6.5: We did what we need to do with congruence testing with right triangles already. We did the HL. This chapter also includes LL (SAS), HA and LA (both AAS). Pythagoreans: 1 represented logic because reason could produce only one consistent body of truths 2 stood for man 3 stood for woman 4 stood f ...
Math 4707 Intro to combinatorics and graph theory
... web, take-home exam, but you are not allowed to collaborate. The instructor is the only human source you are allowed to consult. 1. (15 points) Recall that the Fibonacci numbers are defined by a recurrence Fn+1 = Fn + Fn−1 , with initial conditions F0 = 0, F1 = 1. Without using the recurrence to com ...
... web, take-home exam, but you are not allowed to collaborate. The instructor is the only human source you are allowed to consult. 1. (15 points) Recall that the Fibonacci numbers are defined by a recurrence Fn+1 = Fn + Fn−1 , with initial conditions F0 = 0, F1 = 1. Without using the recurrence to com ...
Hor
... Mersenne primes, Fibonacci sequence, and perfect numbers. Some results are as follows. The Mersenne number 2 n 1 being prime implies that n is prime. Any two consecutive terms in the Fibonacci sequence, defined by the recursion formula an1 an an1 , are relatively prime to each other. An inte ...
... Mersenne primes, Fibonacci sequence, and perfect numbers. Some results are as follows. The Mersenne number 2 n 1 being prime implies that n is prime. Any two consecutive terms in the Fibonacci sequence, defined by the recursion formula an1 an an1 , are relatively prime to each other. An inte ...
Proofs and Proof Methods
... • P(n) → Q(n): Assume that n is even. Then n = 2k for some integer k. Then we compute that n - 1 = 2k - 1 = 2(k - 1) + 1, and by definition n - 1 is odd. • Q(n) → R(n): Assume that n - 1 is odd. Then n - 1 = 2k + 1 for some integer k. So n = 2k + 2 and n2 = (2k + 2)2 = 4k2 + 8k + 4 = 2(2k2 + 4k + 2) ...
... • P(n) → Q(n): Assume that n is even. Then n = 2k for some integer k. Then we compute that n - 1 = 2k - 1 = 2(k - 1) + 1, and by definition n - 1 is odd. • Q(n) → R(n): Assume that n - 1 is odd. Then n - 1 = 2k + 1 for some integer k. So n = 2k + 2 and n2 = (2k + 2)2 = 4k2 + 8k + 4 = 2(2k2 + 4k + 2) ...
Letter to the Editor
... I'm afraid there was an error in the February issue of The Fibonacci Quarterly. Mr. Shallit's proof that phi is irrational is correct up to the point where he claims that 1/0 can't be an integer. He has no basis for making that claim, as 0 was defined as a rational number, not an integer. The proof ...
... I'm afraid there was an error in the February issue of The Fibonacci Quarterly. Mr. Shallit's proof that phi is irrational is correct up to the point where he claims that 1/0 can't be an integer. He has no basis for making that claim, as 0 was defined as a rational number, not an integer. The proof ...
Exponents
... Scientific or Algebraic calculator ALWAYS uses order of operations Arithmetic calculator ALWAYS goes left to right ...
... Scientific or Algebraic calculator ALWAYS uses order of operations Arithmetic calculator ALWAYS goes left to right ...
