Mathematics, 14.02.2021 19:00, janeou17xn
For each positive integer n, consider the pair (3^n −1, 5^n −1). For n = 1, this is the pair (2, 4) and for n = 2, it is (8, 24). Can you find a value for n such that both numbers in the pair (3^n − 1, 5^n − 1) are divisible by d = 7? Can you find more than one such n? Do you think there are finitely or infinitely many n such that 3n − 1 and 5n − 1 are both divisible by d = 7? Why? Explain your reasoning as carefully as you can.
Now, what if we replace d = 7 with d = 11? Or with d = 13? What if we take d = 77
or d = 1001? Describe any patterns you think are interesting.
Answers: 1
Mathematics, 20.06.2019 18:04, Uc34758
Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?
Answers: 2
Mathematics, 21.06.2019 15:20, lambobacon9027
Classify the following triangle check all that apply
Answers: 2
Mathematics, 21.06.2019 18:40, stephen4438
Which of the following represents the range of the graph of f(x) below
Answers: 1
For each positive integer n, consider the pair (3^n −1, 5^n −1). For n = 1, this is the pair (2, 4)...
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